BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nelson Niu (Topos Institute) DTSTART:20261105T200000Z DTEND:20261105T204500Z DTSTAMP:20261030T080954Z UID:ThirdVWDC/1 DESCRIPTION:Title: Loose Yoneda theory for equipments\nby Nelson Niu (Topos Institute) as part of Third Virtual Workshop on Double Categories\n\n\nAbstract\nWhil e applications for double categories and proarrow equipments abound in for mal category theory\, categorical systems theory\, and beyond\, their Yone da theory had only ever been developed for representable functors specifyi ng tight arrows\, by Paré. This is because in general\, there is no ordin ary representable double functor out of a (weak) double category: loose ar rows would need to be sent to tight arrows (functors)\, while tight arrows would need to be sent to loose ones (profunctors). In recent work\, Lambe rt\, Myers\, and Patterson resolve this issue by introducing twisted doubl e functors\, precisely the structure needed for a loose Hom functor. We re view this construction before presenting our Yoneda lemma and embedding fo r these twisted representables out of double categories when they have pro arrow equipments. This material is ongoing joint work with Lambert and Pat terson.\n LOCATION:https://researchseminars.org/talk/ThirdVWDC/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Edward Morehouse DTSTART:20261105T204500Z DTEND:20261105T213000Z DTSTAMP:20261030T080954Z UID:ThirdVWDC/2 DESCRIPTION:Title: Dinaturality for double categories\nby Edward Morehouse as part of T hird Virtual Workshop on Double Categories\n\n\nAbstract\nWe introduce din atural transformations for double categories and show that they enjoy seve ral of the same properties as dinatural transformations for 1-categories\, including subsuming ordinary natural transformations\, composing with the m\, and composing with one another in a suitably groupoidal setting. As a n application\, we show how extranatural transformations for 1-categories can be characterized using dinatural transformations in the double categor y of small categories.\n LOCATION:https://researchseminars.org/talk/ThirdVWDC/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Bryce Goldman (Topos Institute) DTSTART:20261105T213000Z DTEND:20261105T221500Z DTSTAMP:20261030T080954Z UID:ThirdVWDC/3 DESCRIPTION:Title: A Programming Language for Virtual Double Theories\nby Bryce Goldman (Topos Institute) as part of Third Virtual Workshop on Double Categories\ n\n\nAbstract\nLike familiar theories of first-order logic\, the theories of many categorical logics can be specified by a finite presentation of ge nerating symbols and axioms. Each categorical logic is parameterized by a "virtual double theory"\, a kind of virtual equipment\, which can be used to construct type theories over their models. This is especially useful in software systems based on categorical logic\, such as CatColab\, where mo dels of various domain-specific logics are supported by type systems built uniformly from these virtual double theories.\n\nBuilding on prior work b y Hayato Nasu on a type theory for virtual double categories\, we introduc e foundations for a programming language for specifying virtual double the ories\, and present a prototype compiler. We highlight connections with or dered linear logic\, and propose a novel operational semantics that captur es the universal properties of loose units through a directed reduction pr ocedure.\n LOCATION:https://researchseminars.org/talk/ThirdVWDC/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Lambert (Norwich University) DTSTART:20261105T221500Z DTEND:20261105T230000Z DTSTAMP:20261030T080954Z UID:ThirdVWDC/4 DESCRIPTION:Title: Quantification in Double-Categorical Database Schemas\nby Michael La mbert (Norwich University) as part of Third Virtual Workshop on Double Cat egories\n\n\nAbstract\nThe introduction of right adjoints to substitution in the equipment structure of a double olog allows modeling of relational division\, an advanced query used in relational databases\, for example\, to compare a shopping list against an inventory. This talk with review rel ational division and show how it can be captured using these right adjoint s in double-categorical database schemas. Asking for these adjoints enrich es these structures in other ways. For example\, such double ologs model f ull first-order modal logic\, and thus description logic\, and allow compo und database queries involving disjunction\, implication and negation. Bec k-Chevalley and Frobenius Reciprocity are automatically satisfied in any s uch database schema and can be seen to be query optimization rules that ar e thus provably error-free.\n LOCATION:https://researchseminars.org/talk/ThirdVWDC/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Maru Sarazola (University of Minnesota) DTSTART:20261106T160000Z DTEND:20261106T164500Z DTSTAMP:20261030T080954Z UID:ThirdVWDC/5 DESCRIPTION:Title: K-theory of monoids via double categories\nby Maru Sarazola (Univers ity of Minnesota) as part of Third Virtual Workshop on Double Categories\n \n\nAbstract\nFor any finite group G\, there is a well-known formula that computes the algebraic K-theory of the category of finite G-sets\; i.e. fi nite sets with a G-action. Interestingly\, if we drop the existence of inv erses and swap G by a monoid M\, things get a lot more complicated and eac h step in the proof independently breaks down!\n\nIn this talk\, I will ex plain how we can save the day by considering a double category of M-sets i nstead. Along the way\, I will try to outline some recent developments in algebraic K-theory that make heavy use of double categories. \n\nThe talk won't assume any knowledge of K-theory\, and will only assume a working un derstanding of what a double category is.\n LOCATION:https://researchseminars.org/talk/ThirdVWDC/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Aaron David Fairbanks (Dalhousie University) DTSTART:20261106T164500Z DTEND:20261106T173000Z DTSTAMP:20261030T080954Z UID:ThirdVWDC/6 DESCRIPTION:Title: Doubly weak double categories\nby Aaron David Fairbanks (Dalhousie U niversity) as part of Third Virtual Workshop on Double Categories\n\n\nAbs tract\nDouble categories are typically weak in one direction: the horizont al (or "loose") 1-cells compose weakly associatively as in a bicategory (a .k.a. weak 2-category)\, whereas the vertical (or "tight") 1-cells compose strictly associatively as in a strict 2-category. There have been various attempts to define double categories with weakly associative composition in both directions. This is desirable in order to capture a broader range of examples\, as well as to obtain a more symmetric theory. What is puzzli ng is that trying to straightforwardly generalize the usual definition lea ds into deadlock around coherence conditions.\n\nWe introduce a surprising ly easy definition that involves no coherence conditions. It arises as the double-categorical analogue of a surprisingly easy definition of bicatego ry that involves no coherence conditions. We then connect this definition to other definitions that are more analogous to the usual definition of bi category. In particular we show our doubly weak double categories are equi valent to Verity's double bicategories satisfying a mild condition that al ready appears in the literature\, and they are equivalent to Garner's cubi cal bicategories satisfying a similar condition. Joint work with Michael S hulman.\n LOCATION:https://researchseminars.org/talk/ThirdVWDC/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Kurz (Chapman University) DTSTART:20261106T173000Z DTEND:20261106T181500Z DTSTAMP:20261030T080954Z UID:ThirdVWDC/7 DESCRIPTION:Title: From Zero-Dimensional to Continuous Dualities: A Double-Categorical Acco unt\nby Alexander Kurz (Chapman University) as part of Third Virtual W orkshop on Double Categories\n\n\nAbstract\nWe investigate how to systemat ically construct continuous dualities from zero-dimensional dualities\, em ploying well-known methods from algebra\, topology\, category theory\, and domain theory. While our method is general\, this paper focusses on the m ove from Stone spaces to compact Hausdorff spaces and the move from Priest ley spaces to compact ordered Hausdorff spaces. The engine of our approach is Stone duality for relations: on the space side quotienting by a preord er turns zero-dimensional spaces into continuous ones\, while distributive lattices with a proximity relation are their algebraic duals. Our duality for relations is inherently order-enriched. Double categories organise bo th functional and relational morphism in the same structure. The move from zero-dimensional to continuous dualities is then a three-step constructio n: extend a duality from functional to relational morphism\, split idempot ents\, restrict to maps.\n LOCATION:https://researchseminars.org/talk/ThirdVWDC/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Claudio Pisani DTSTART:20261106T181500Z DTEND:20261106T190000Z DTSTAMP:20261030T080954Z UID:ThirdVWDC/8 DESCRIPTION:Title: Unbiased Algebra\nby Claudio Pisani as part of Third Virtual Worksho p on Double Categories\n\n\nAbstract\nThe main trust of the unbiased appro ach to algebra is that operations on a set X form a category whose objects are (finite) families I → X and are indexed by functions I → J. Furth ermore\, operations can be reindexed along pullbacks in finite sets.\n\nTh is inevitably leads to the notion of unbiased symmetric multicategory [1]: a double category M with parallel sums\, along with a sum-preserving doub le functor M → Pb (to the double category of pullback squares in finite sets) which is a discrete fibration in the tight direction. The loose arro ws of M should be thought of as the abstract operations of the algebraic t heory\, while tight arrows and cells give reindexing.\n\nOperads are the s ingle-sorted theories\, namely those M with just an object over a terminal set. If S is a species of structure in the sense of Joyal\, an S-function is a function endowed with an S-structure on each of its fibers. For many basic species\, S-functions can be naturally composed\, so that they form the operations of an operad\; in fact all operads arise in this way.\n\nA n algebra for M is itself a symmetric multicategory A with a double functo r A → M which is a discrete opfibration in the loose direction. The loos e arrows of A are the (concrete) operations of the algebra\, indexed by th e abstract operations in M. For instance\, an algebra for the terminal ope rad Pb → Pb is (the unbiased form of) a commutative monoid X: a concret e operation evaluates a family I → X along a function I → J (the under laying abstract operation) to give a family J →X. The algebras for the o perad Tot\, associated to the species of total orders\, are plain monoids: operations evaluate families along functions with totally ordered fibers. \n\nIt is well-known that operads (or more generally symmetric multicatego ries) do not capture all kinds of ordinary algebraic theories since\, roug hly\, one cannot duplicate or delete variables. To this end one introduces cartesian multicategories\, which have a very neat definition in the pres ent context. Namely\, they are the algebras for a natural monad cart on sy mmetric multicategories: the loose arrows of cart M are spans (actually\, "enhanced" spans [1]) formed by a tight arrow and a loose arrow in M. Thes e are composed in the usual way for spans\, except that we use M-cells in place of pullbacks. Thus\, a cartesian structure cart M → M provides a w ay to "sum" an operation along a function to give a new operation. \n\nMul ticategories which are both cartesian and cocartesian (a.k.a. sequential [ 2]) amount to categories enriched in commutative monoids. In particular\, cartesian and cocartesian operads amount to rigs. In the operad associated to a rig R\, an operation α over a function I → J\, is a family I → R\, and composition is given by multiplication in the underlying monoid (a s in the discrete distribution monad). The sum of α along f : I → K is obtained by adding the elements in the fibers of f.\n\nAlgebras for a cart esian operad M are required to satisfy a further compatibility condition\, corresponding to the fact that they can be seen as morphisms of cart-alge bras from M to the endomorphism operad End(X). The algebras for the cartes ian operad associated to a rig R are the R-modules.\nFor an operad M\, the free M-algebra monad is given again by spans in M but\, in a sense\, dual ly to cart. If M is cartesian\, free M-algebras are obtained by quotientin g with respect to a natural equivalence on spans. Similarly\, given N → M\, the relatively free M-algebras are obtained by quotienting spans in M. \nWe also illustrate the connections between cartesian operads and Lawvere theories.\n\nThe overall purpose of the talk is to show how the unbiased approach\, by avoiding the awkwardness which inevitably arises from an unn atural skeletal indexing\, turns out to be rather effective and opens up n ew perspectives.\n\n[1] C. Pisani\, Unbiased multicategory theory\, Theory and Applications of Categories 44 (2025)\, 826–868.\n[2] C. Pisani\, Se quential multicategories\, Theory and Applications of Categories 29 (2014) \, 496–541.\n LOCATION:https://researchseminars.org/talk/ThirdVWDC/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Matt Earnshaw (University of Tartu) DTSTART:20261110T120000Z DTEND:20261110T124500Z DTSTAMP:20261030T080954Z UID:ThirdVWDC/9 DESCRIPTION:Title: Representability of Generalized Multicategories\nby Matt Earnshaw (U niversity of Tartu) as part of Third Virtual Workshop on Double Categories \n\n\nAbstract\nA multicategory has morphisms whose domains are lists of o bjects. A generalized multicategory has morphisms whose domains have a sha pe specified by a monad T. Representability concerns the equivalence betwe en structure defined by universal property\, and structure defined coheren tly: classically\, this is Hermida’s equivalence between representable m ulticategories and monoidal categories. The theory of representability for generalized multicategories allow us to capture many results of this gene ral shape. Seen through the lens of double category theory\, to ask when a T-multicategory is representable is to ask when it is the underlying loos e T-coalgebra of a pseudo-T-algebra. This talk will introduce the basic th eory\, such as the monadic adjunction between T-algebras and T-multicatego ries. This is based on work-in-progress with Nathanael Arkor.\n LOCATION:https://researchseminars.org/talk/ThirdVWDC/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Bojana Femić (Mathematical Institute of Serbian Academy of Scienc es and Arts) DTSTART:20261110T124500Z DTEND:20261110T133000Z DTSTAMP:20261030T080954Z UID:ThirdVWDC/10 DESCRIPTION:Title: Para construction for double categories\nby Bojana Femić (Mathemat ical Institute of Serbian Academy of Sciences and Arts) as part of Third V irtual Workshop on Double Categories\n\n\nAbstract\nThe Para construction is an important concept in Computer Science. Taking it as motivation\, we carried out a purely categorical study in the following direction. \n\nWe introduce Para and coPara double categories for double categories\, extend ing the construction from [1] carried out for 1-categories. The latter use s actegories over monoidal categories\, while we use a horizontal action o f a horizontally monoidal double category M on a double category D. Our ma in result is the following. \n\nFor horizontally monoidal double categorie s M and D with a horizontal lax action F (of M on D) such that M is horizo ntally double braided\, we prove that the following are equivalent: \n1. t here is a structure of a lax monoidal horizontal lax action\, \n2. there i s a structure of a bistrong and commutative horizontal lax action\, \n3. t here is a purely central horizontally premonoidal structure on $\\mathrm{c oPara}_M(D)$ (with trivial 2-cells (u\,U) )\, \n4. there is a horizontally monoidal structure on $\\mathrm{coPara}_M(D)$ extending that on D.\n\nAs it occurs in the Kleisli construction\, the "parametric" 1-cells must live in the loose direction. For this reason in the above structures the horiz ontal (our loose) direction appears. As a matter of fact\, the coPara cons truction generalizes the Kleisli construction in the same lines as an acti on of a monoidal (double) category generalizes a (double) monad. \nShulman [5] has introduced the notion of a monoidal double category via vertical (tight) monoidality transformations\, so that assuming existence of compan ions (for the tight 1-cell components of those transformations) one retrie ves a monoidal bicategory out of the latter\, at a much lower price than o ne would have expected. In [2] we studied the relation between premonoidal and monoidal structures on a double category\, where we introduced the no tion of a premonoidal double category using the vertical direction\, too. For the purpose of the equivalence of 3. and 4\, above we introduced both notions in the horizontal sense and have also studied under which companio n-lifting assumptions vertical structures yield the corresponding horizont al ones. The equivalence of 1.\, 2. and 4. is our extension to double cate gories of a bicategorical result from [4]. The implication 1.=> 4. truncat ed to 1-categories was concluded in [1] via a fully different approach. We also give an overview of the lifting of vertical to horizontal structures from the perspective of llocally cubical bicategories from [3]. \n\n[1] M . Capucci\, D. Jaz Myers\, "Contextads as Wreaths\; Kleisli\, Para\, and S pan Constructions as Wreath Products"\, preprint. \n\n[2] B. Femić\, "Kle isli and premonoidal double categories"\, Mathematical Structures in Compu ter Science.\n\n[3] R. Garner\, N. Gurski\, "The low-dimensional structure s formed by tricategories".\n\n[4] H. Paquet\, P. Saville\, "Effectful sem antics in 2-dimensional categories: strong\, commutative\, and concurrent pseudomonads"\, LICS '24: Proceedings of the 39th Annual ACM/IEEE Symposiu m on Logic in Computer Science Article 61\, 1 - 15. \n\n[5] M. Shulman\, " Constructing symmetric monoidal bicategories".\n LOCATION:https://researchseminars.org/talk/ThirdVWDC/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Robin Jourde (Université Savoie Mont Blanc) DTSTART:20261110T133000Z DTEND:20261110T141500Z DTSTAMP:20261030T080954Z UID:ThirdVWDC/11 DESCRIPTION:Title: Relational theories and their locally presentable categories of models\ , with applications to skeletal semantics\nby Robin Jourde (Universit é Savoie Mont Blanc) as part of Third Virtual Workshop on Double Categori es\n\n\nAbstract\nWe study virtual double theories\, which are a virtual-d ouble-categorical extension of Lawvere theories\, allowing for the interpr etation of some morphisms as relations. We first prove that the category o f models of any virtual double theory is locally presentable. We then intr oduce a notion of presentation for virtual double theories\, analogous to the notion of presentation of a Lawvere theory by generators and relations . Finally\, we apply these results to design a mathematical foundation for skeletal semantics\, a software framework for specifying and analysing pr ogramming languages. We show that skeletal specifications may be interpret ed as presentations of virtual double theories\, so that the category of m odels of the virtual double theory associated to any presentation provides the intended language with initial algebra semantics.\n LOCATION:https://researchseminars.org/talk/ThirdVWDC/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Jana Nickel (University of Hamburg) DTSTART:20261110T141500Z DTEND:20261110T150000Z DTSTAMP:20261030T080954Z UID:ThirdVWDC/12 DESCRIPTION:Title: Transpose-closed virtual double categories and coend calculus\nby J ana Nickel (University of Hamburg) as part of Third Virtual Workshop on Do uble Categories\n\n\nAbstract\nThe talk is based on a project joint with N athanael Arkor. We lay the foundations for a coend calculus in the framewo rk of virtual double categories. To this end\, we establish the concept of a transpose-closed virtual equipment and introduce the notion of a coend for tight arrows. The goal is to develop a coend calculus for transpose-cl osed virtual equipments in a similar manner as the calculus of ends for ca tegories enriched over the bicategory of spans in a topos due to Betti and Walters (“The calculus of ends over a base topos”\, JPAA\, 1989) and to recover some prominent results\, such as the Fubini theorem for coends. To cite an example\, we will consider the virtual equipment Span(E) of sp ans in an ordinary category E with pullbacks and describe a transpose-clos ed structure on it.\n LOCATION:https://researchseminars.org/talk/ThirdVWDC/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Hayato Nasu (Dalhousie University) DTSTART:20261110T150000Z DTEND:20261110T154500Z DTSTAMP:20261030T080954Z UID:ThirdVWDC/13 DESCRIPTION:Title: Virtual double categories of relations relative to fibrations\nby H ayato Nasu (Dalhousie University) as part of Third Virtual Workshop on Dou ble Categories\n\n\nAbstract\nThe double category of relations is one of t he most beloved examples of double categories\, with many variations\, suc h as frame-valued relations and relations with respect to different kinds of monomorphisms (the right class of a factorization system). Such double categories are systematically captured by Shulman's Fr construction\, whic h produces a double category of relations internal to a certain class of m onoidal fibrations. \n\nIn this talk\, I will present a generalization of this construction that produces a virtual double category of relations\, w here loose morphisms are not required to compose. I will also give a chara cterization of the class of fibrations called elementary existential fibra tions as those for which the induced virtual double category is a cartesia n equipment. In fact\, these fibrations and cartesian equipments with one additional assumption form biequivalent 2-categories. If time permits\, I will discuss a further generalization of this construction that captures m ore than binary relations\, which is ongoing joint work with Aaron Fairban ks.\n LOCATION:https://researchseminars.org/talk/ThirdVWDC/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Maxine Calle (University of Bonn\, Mathematical Institute) DTSTART:20261111T080000Z DTEND:20261111T084500Z DTSTAMP:20261030T080954Z UID:ThirdVWDC/14 DESCRIPTION:Title: On the K-theory of cut-and-paste manifolds\nby Maxine Calle (Univer sity of Bonn\, Mathematical Institute) as part of Third Virtual Workshop o n Double Categories\n\n\nAbstract\nGiven two manifolds M and N\, one can a sk whether it is possible to cut M up into pieces and reassemble them to o btain N. This “cut-and-paste” (SK) relation fits into the framework of scissors congruence K-theory\, which is an extension of higher algebraic K-theory to more general settings. In this talk\, we will discuss a new mo del for the cut-and-paste K-theory of manifolds and analyze its properties . Along the way\, we will highlight how double categorical techniques may be applied to scissors congruence K-theory more generally. This talk is ba sed on joint work with Maru Sarazola.\n LOCATION:https://researchseminars.org/talk/ThirdVWDC/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuto Kawase (Research Institute for Mathematical Sciences\, Kyoto University) DTSTART:20261111T084500Z DTEND:20261111T093000Z DTSTAMP:20261030T080954Z UID:ThirdVWDC/15 DESCRIPTION:Title: Double categories of profunctors\nby Yuto Kawase (Research Institut e for Mathematical Sciences\, Kyoto University) as part of Third Virtual W orkshop on Double Categories\n\n\nAbstract\nIn this talk\, I will introduc e a new notion of double-categorical colimits and use it to characterize v irtual double categories of enriched categories\, functors\, and profuncto rs. These colimits have a property analogous to the effectiveness of equiv alence relations\, which plays a crucial role in reconstructing enriched c ategories in the characterization. This talk is based on my recent paper.\ n LOCATION:https://researchseminars.org/talk/ThirdVWDC/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Sarah Dukic (Leiden University) DTSTART:20261111T093000Z DTEND:20261111T101500Z DTSTAMP:20261030T080954Z UID:ThirdVWDC/16 DESCRIPTION:Title: Formal and Enriched Coalgebra\nby Sarah Dukic (Leiden University) a s part of Third Virtual Workshop on Double Categories\n\n\nAbstract\nIn th is talk\, we present a formal theory of coalgebras\, formulated internally in a double category. Our primary goal is to instantiate this to the enri ched setting\, providing a general theory of enriched coalgebras. To this end\, we characterise categories of coalgebras abstractly as universal obj ects in double categories\, adapting Kelly’s 2-categorical notion of ins erters to double categories by instantiating them in the underlying morphi sm 2-category. A major advantage of this double-categorical formulation is that it allows us to prove that coalgebra objects inherit weighted colimi ts from the base category\, without the assumption of cartesian closedness . Our main result is that coalgebra objects are given functorially by a li mit-preserving double functor\, which comes equipped with a natural projec tion which creates weighted colimits. We will apply these results by insta ntiating them to several enriched settings\, study coalgebras in the doubl e category of fibrations\, and work towards a framework for coalgebraic lo gic internal to double categories.\n LOCATION:https://researchseminars.org/talk/ThirdVWDC/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Theofilos Tsantilas (National Technical University of Athens) DTSTART:20261111T101500Z DTEND:20261111T110000Z DTSTAMP:20261030T080954Z UID:ThirdVWDC/17 DESCRIPTION:Title: The double category of restriction distributors\nby Theofilos Tsant ilas (National Technical University of Athens) as part of Third Virtual Wo rkshop on Double Categories\n\n\nAbstract\nRestriction categories were int roduced by Cockett and Lack as a framework where one could study the notio n of "partially defined" maps in a systematic way. In this talk\, which is based on ongoing work with Nathanael Arkor\, Yorgo Chamoun\, Bryce Clarke \, Vit Jelinek and Hayato Nasu and was initiated as a project in the 2026 Adjoint School\, we will define restriction categories and see how these w ere seen as categories enriched in a (weak) double category by Cockett and Garner. Furthermore\, we shall present how this viewpoint could be extend ed to an equivalence of double categories and what new prospects could thi s entail.\n LOCATION:https://researchseminars.org/talk/ThirdVWDC/17/ END:VEVENT END:VCALENDAR