BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:P. Jacqmin (Royal Military Academy) DTSTART:20240410T130000Z DTEND:20240410T134000Z DTSTAMP:20260422T225843Z UID:ItaCa-Fest-2024/1 DESCRIPTION:Title: Surjection-like classes of morphisms\nby P. Jacqmin (Royal Mil itary Academy) as part of ItaCa Fest 2024\n\n\nAbstract\nMany classes of e pimorphisms are considered in the literature with the aim of generalizing surjective functions from the category Set of sets to an arbitrary categor y. However\, some of them fail to have specific desirable properties.\nIn this talk\, we are interested in classes of morphisms which interact with finite limits as surjections do in Set. More precisely\, we study classes of morphisms in finitely complete categories which admit a "good" embeddin g in a presheaf category. By good embedding\, we mean a functor which pres erves and reflects finite limits and the classes of morphisms involved. We will examine both the conservative faithful and the fully faithful cases. \nOur main result is a complete characterization of those classes of morph isms via simple and well-known properties.\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2024/1/ END:VEVENT BEGIN:VEVENT SUMMARY:A. Cigoli (Università degli Studi di Torino) DTSTART:20240410T142000Z DTEND:20240410T150000Z DTSTAMP:20260422T225843Z UID:ItaCa-Fest-2024/2 DESCRIPTION:Title: From Yoneda's additive regular spans to fibred cartesian monoidal opfibrations\nby A. Cigoli (Università degli Studi di Torino) as part of ItaCa Fest 2024\n\n\nAbstract\nIt is well known that group cohomology can be interpreted in terms of equivalence classes of crossed extensions\, the abelian group structure being given by the so-called Baer sums. By an alogy\, an intrinsic definition of cohomology in strongly semi-abelian cat egories\, or more generally in exact Mal'tsev categories (Bourn-Rodelo)\, is given. In this talk\, I will explain how Baer sums can be formally deri ved from the fibred/cofibred nature of the category of all crossed extensi ons of a given length. This point of view turns out to be very close to Yo neda's theory of Ext groups. We will see how his notion of additive regula r span is actually an instance of fibred cartesian monoidal opfibration. T ime permitting\, I will give some hint on how this formal point of view ca n be carried on to a 2-dimensional level\, thus giving a notion of cohomol ogy 2-group.\n\n\n(based on joint works with S. Mantovani\, G. Metere and E.M. Vitale)\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2024/2/ END:VEVENT BEGIN:VEVENT SUMMARY:M. Mancini (Università di Palermo) DTSTART:20240410T134000Z DTEND:20240410T142000Z DTSTAMP:20260422T225843Z UID:ItaCa-Fest-2024/3 DESCRIPTION:Title: On the representability of actions of non-associative algebras \nby M. Mancini (Università di Palermo) as part of ItaCa Fest 2024\n\n\nA bstract\nIt is well known that in the semi-abelian category Grp of groups\ , internal actions are represented by automorphisms. This means that the c ategory Grp is action representable and the actor of a group X is the grou p Aut(X). The notion of action representable category has proven to be qui te restrictive: for instance\, if a non-abelian variety of non-associative algebras\, over an infinite field of characteristic different from two\, is action representable\, then it is the category of Lie algebras. More re cently G. Janelidze introduced the notion of weakly action representable c ategory\, which includes a wider class of categories.\n\nIn this talk we s how that for an algebraically coherent variety of algebras and an object X of it\, it is always possible to construct a partial algebra E(X)\, calle d external weak actor of X\, which allows us to describe internal actions on X. Moreover\, we show that the existence of a weak representation is co nnected to the amalgamation property and we give an application of the con struction of the external weak actor in the context of varieties of unitar y algebras.\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2024/3/ END:VEVENT BEGIN:VEVENT SUMMARY:F. Rota (University of Glasgow) DTSTART:20240507T134000Z DTEND:20240507T142000Z DTSTAMP:20260422T225843Z UID:ItaCa-Fest-2024/4 DESCRIPTION:Title: Exceptional collections and pseudolattices in mirror symmetry\ nby F. Rota (University of Glasgow) as part of ItaCa Fest 2024\n\n\nAbstra ct\nIn the 1990s\, theoretical physicists correctly predicted curve counts in an algebraic variety (a quintic threefold X) inferring them from a “ mirror variety” Y. This was the start of mirror symmetry - a field of al gebraic geometry that investigates how to construct mirrors and how to mak e the duality precise. A modern incarnation of the theory is the homologic al mirror symmery (HMS) conjecture by Kontsevich\, which states that the d uality first observed geometrically reflects an equivalence between a cate gory built from X and one obtained from Y.\n\nDescribing and motivating so me of the structures carried by these categories\, I’ll briefly mention how to interpret the HMS equivalence as a quasi-isomorphism of Ainfty-alge bras\, and then elaborate on necessary conditions for the equivalence\, wh ich rephrase the question into multilinear algebra.\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2024/4/ END:VEVENT BEGIN:VEVENT SUMMARY:V. Ozornova (Max Planck Institute for Mathematics) DTSTART:20240507T142000Z DTEND:20240507T150000Z DTSTAMP:20260422T225843Z UID:ItaCa-Fest-2024/5 DESCRIPTION:Title: Equivalences in higher categories\nby V. Ozornova (Max Planck Institute for Mathematics) as part of ItaCa Fest 2024\n\n\nAbstract\nThere are different notions of ‘sameness’ arising in mathematics. The first one we usually encounter is equality of elements in a set. In our ‘dail y life’\, we are used to identify isomorphic objects\, and we are secret ly doing so in our favorite category. For categories themselves\, we look for equivalences between those. But when should we consider two 2-categori es to be ‘the same’? And how does the pattern continue? \n\nThis talk is based upon joint work with Amar Hadzihasanovich\, Félix Loubaton and M artina Rovelli.\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2024/5/ END:VEVENT BEGIN:VEVENT SUMMARY:L. Santocanale (Aix-Marseille University) DTSTART:20240605T150000Z DTEND:20240605T154000Z DTSTAMP:20260422T225843Z UID:ItaCa-Fest-2024/6 DESCRIPTION:Title: Complete congruences of completely distributive lattices\nby L . Santocanale (Aix-Marseille University) as part of ItaCa Fest 2024\n\n\nA bstract\nAll the binomial lattices [1] embed into the quantale Q(I) of sup -preserving endomaps\nof the unit interval. Elements of these lattices can be seen as monotone paths from (0\; 0)\nto (1\; 1)\, discrete paths for t he binomial lattices\, continuous paths for Q(I) [2]. We aim\nat extending a natural geometric interpretation of lattice congruences of binomial lat tices\nto congruences of Q(I). This is\, in particular\, a completely dist ributive lattice.\n\nRelying on Lawson-Hoffmann duality [3\, 4]\, we chara cterise those maps between con-\ntinuous domains that give rise to complet e maps between completely distributive lattices.\nThis allows to describe the complete congruences of an arbitrary completely distributive\nlattice by means of an interior operator on the collection of the closed sets of a n associated\ntopological space. In particular\, we show that these congru ences form a frame. We study\nthis frame for the unit interval lattice\, a rguing that this frame is not a Boolean algebra\,\nnor it is a (co)spatial . For the quantale Q(I)\, we give a geometrical interpretation of these\nc ongruences by means of directed homotopies.\n\n[1] Bennett\, M.K.\, Birkho ff\, G.: Two families of Newman lattices. Algebra Universalis 32(1)\,\n115 -144 (1994).\n\n[2] Santocanale\, L.\, Gouveia\, M.J.: The continuous weak order. Journal of Pure and Applied\nAlgebra 225\, 106472 (2021).\n\n[3] L awson\, J.D.: The duality of continuous posets. Houston J. Math. 5\, 357-3 86 (1979).\n\n[4] Hoffmann\, R.E.: Continuous posets\, prime spectra of co mpletely distributive complete lat-\ntices\, and Hausdorff compactificatio ns. Continuous lattices\, Proc. Conf.\, Bremen 1979\, Lect.\nNotes Math. 8 71\, 159-208 (1981).\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2024/6/ END:VEVENT BEGIN:VEVENT SUMMARY:J. Weinberger (Johns Hopkins University) DTSTART:20240605T154000Z DTEND:20240605T162000Z DTSTAMP:20260422T225843Z UID:ItaCa-Fest-2024/7 DESCRIPTION:Title: The dependent Gödel fibration\nby J. Weinberger (Johns Hopkin s University) as part of ItaCa Fest 2024\n\n\nAbstract\nGödel‘s Dialect ica proof interpretation from the 1950s was used as a tool for consistency proofs. In the late 80s\, de Paiva introduced several categorified versio n of it\, leading to notions of Dialectica categories. These\, in turn\, h ave later been generalized to the level of fibered categories. We present a characterization of Dialectica fibrations via the notion of Gödel fibra tion\, generalizing earlier work by Spadetto—Trotta—de Paiva. This is joint work with Davide Trotta and Valeria de Paiva.\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2024/7/ END:VEVENT BEGIN:VEVENT SUMMARY:D. Stein (Radboud University Nijmegen) DTSTART:20240925T130000Z DTEND:20240925T134000Z DTSTAMP:20260422T225843Z UID:ItaCa-Fest-2024/8 DESCRIPTION:Title: Random Variables and Categories of Abstract Sample Spaces\nby D. Stein (Radboud University Nijmegen) as part of ItaCa Fest 2024\n\n\nAbs tract\nTwo high-level "pictures" of probability theory have emerged: one t hat takes as central the notion of random variable\, and one that focuses on channels and distributions (Markov kernels).\n\nWhile the channel-based picture has been captured and widely generalized using the notion of Mark ov category\, the categorical analogue of the random variable picture is l ess clear. I will discuss the conceptual interplay between the two picture s: A crucial step is to understand the category of sample spaces associate d to a given Markov category. This construction gives rise to a host of we ll-known examples. Building on the work of Simpson\, we can describe rando m variables in the sheaf topos over those sample spaces.\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2024/8/ END:VEVENT BEGIN:VEVENT SUMMARY:D. Ahman (University of Tartu) DTSTART:20240925T134000Z DTEND:20240925T142000Z DTSTAMP:20260422T225843Z UID:ItaCa-Fest-2024/9 DESCRIPTION:Title: Comodule Representations of Second-Order Functionals\nby D. Ah man (University of Tartu) as part of ItaCa Fest 2024\n\n\nAbstract\nIn inf ormation-theoretic terms\, a map is continuous when a finite amount of inf ormation about the input suffices for computing a finite amount of informa tion about the output. Already Brouwer observed that this allows one to re present a continuous functional from sequences to numbers with a certain w ell-founded question-answer tree.\n\nIn type theory\, a second-order funct ional is a (dependently typed) map\n\nF : (∏(a : A) . P a) → (∏(b : B) . Q b).\n\nIts continuity is once again witnessed by (B-many) well-foun ded trees whose nodes are “questions” a : A\, the branches are indexed by “answers” p : P a\, and the leaves are “results” Q b. In this work\, we observe that such tree representations can be expressed in purel y category-theoretic terms\, using the notion of right T-comodules for the monad T of well-founded trees on the category of containers. A tree repre sentation for F is then just a Kleisli map for the monad T.\n\nDoing so ex poses a rich underlying structure\, and immediately suggests generalisatio ns: any right T-comodule for any monad T on containers gives rise to a rep resentation theorem for second-order functionals. We give several examples of these\, ranging from finitely supported functionals\, to functionals t hat can query their input just once (or sometimes not at all)\, to functio nals that can additionally interact with their environment\, to partial fu nctionals\, to observing that any functional can be trivially represented by itself.\n\nThis is joint work with Andrej Bauer from the University of Ljubljana.\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2024/9/ END:VEVENT BEGIN:VEVENT SUMMARY:M. Di Meglio (University of Edinburgh) DTSTART:20240925T142000Z DTEND:20240925T150000Z DTSTAMP:20260422T225843Z UID:ItaCa-Fest-2024/10 DESCRIPTION:Title: Abstraction of contraction\nby M. Di Meglio (University of Ed inburgh) as part of ItaCa Fest 2024\n\n\nAbstract\nThe theory of contracti ons on a Hilbert space plays an important role in modern functional analys is. It is built upon Sz.-Nagy's unitary dilation theorem\, which says that every contraction on a Hilbert space admits a minimal unitary dilation (a unitary dilation of a contraction T: X → X is a unitary U: Y → Y on a Hilbert space Y containing X via an isometry M: X → Y such that T = M*U M). This talk is about an abstraction of the notion of contraction to suit ably nice *-categories\, and will build to a category-theoretic proof of a variant of Sz.-Nagy's theorem.\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2024/10/ END:VEVENT BEGIN:VEVENT SUMMARY:J. Bourke (Masaryk University) DTSTART:20241022T130000Z DTEND:20241022T134000Z DTSTAMP:20260422T225843Z UID:ItaCa-Fest-2024/11 DESCRIPTION:Title: Bicategorical enrichment in algebra\nby J. Bourke (Masaryk Un iversity) as part of ItaCa Fest 2024\n\n\nAbstract\nIn category theory\, s ometimes one does not wish to work with categories per se but instead cate gories over a fixed base. Such concrete categories can be viewed as catego ries enriched in a quantoloid\, a certain bicategory. Garner showed this p erspective is illuminating\, using it to characterise topological categori es as bicategory-enriched categories which are total.\n\nIn this talk\, I will explain how the same enrichment is useful in algebra\, where we also sometimes work over a fixed base. We will use the bicategorically-enriched perspective to show that Eilenberg-Moore categories of monads are free co completions of their Kleisli categories\, which is false from the traditio nal point of view\, and use this to give a nice proof of Beck's monadicity theorem. This is a report on ongoing work with Soichiro Fujii.\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2024/11/ END:VEVENT BEGIN:VEVENT SUMMARY:G. Tendas (University of Manchester) DTSTART:20241022T134000Z DTEND:20241022T142000Z DTSTAMP:20260422T225843Z UID:ItaCa-Fest-2024/12 DESCRIPTION:Title: Regular theories from the enriched point of view\nby G. Tenda s (University of Manchester) as part of ItaCa Fest 2024\n\n\nAbstract\nIn logic\, regular theories are those whose axioms are built from atomic form ulas using conjunctions and existential quantifiers. The categories of mod els of such theories have been widely studied and characterised in purely category theoretical terms through the notion of injectivity class and thr ough certain closure properties\, that I will recall during the talk.\n\nW hen moving to the context of enriched category theory\, a corresponding no tion of "enriched injectivity class" has been studied by several authors\, but no enriched notion of regular logic was considered in the literature before. The aim of this talk\, which is based on joint work with Rosicky\, is to fill this gap by introducing a version of "enriched regular logic" that interacts well with the category theoretical counterparts mentioned a bove. I will also explain how this is related to the internal logic of a t opos\, and that internal to Banach and metric spaces.\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2024/12/ END:VEVENT BEGIN:VEVENT SUMMARY:L. Mesiti (University of Leeds) DTSTART:20241022T142000Z DTEND:20241022T150000Z DTSTAMP:20260422T225843Z UID:ItaCa-Fest-2024/13 DESCRIPTION:Title: Towards elementary 2-toposes\nby L. Mesiti (University of Lee ds) as part of ItaCa Fest 2024\n\n\nAbstract\nIn this talk we will discuss which axioms we should require for a good notion of 2-categorical element ary topos. 2-dimensional elementary topos theory has originated with the w ork of Weber\, who proposed to upgrade subobject classifiers to discrete o pfibration classifiers. In the archetypal case of Cat\, the discrete opfib ration classifier is exhibited by the Grothendieck construction\, suggesti ng that we can think of 2-dimensional classifiers as internal Grothendieck constructions in a 2-category. The theory of elementary 2-toposes has the n been further developed in my PhD thesis\, where I proposed a stronger be tter-behaved notion of discrete opfibration classifier called good 2-class ifier. We will see that a powerful theorem of reduction of the study of 2- dimensional classifiers to dense generators provides a good 2-classifier i n the 2-category of stacks over a site. Exactly as sheaves give Grothendie ck toposes\, stacks give 2-dimensional Grothendieck toposes and they shoul d thus be a preeminent example of elementary 2-topos. We can then study th is preeminent example to try and understand which further axioms we should require to reach a notion of elementary 2-topos.\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2024/13/ END:VEVENT BEGIN:VEVENT SUMMARY:N. Carissimi (Université de Lille) DTSTART:20241120T140000Z DTEND:20241120T144000Z DTSTAMP:20260422T225843Z UID:ItaCa-Fest-2024/14 DESCRIPTION:Title: Enriched bicategories for enrichies bi(co)ends\nby N. Carissi mi (Université de Lille) as part of ItaCa Fest 2024\n\n\nAbstract\nTwo ma in generalizations of category theory are bicategories and enriched catego ries. The first one allows morphisms one level up\, the other one allows m orphisms to be objects in any monoidal category. This talk will be about w hat happens if we do the two at the same time. We will see the notion of m onoidal bicategory and the main available results and tools (such as stric tification and string diagrammatic language) with which enriched bicategor ies and their rich algebraic structures can be tamed. Thus\, the assumptio n of a suitable notion of braiding on the base monoidal bicategory will al low to generalize the fundamental constructions of forming the opposite an d the tensor product of enriched bicategories\, and possibly more.\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2024/14/ END:VEVENT BEGIN:VEVENT SUMMARY:S. Wolf (Universität Regensburg) DTSTART:20240507T130000Z DTEND:20240507T134000Z DTSTAMP:20260422T225843Z UID:ItaCa-Fest-2024/15 DESCRIPTION:Title: Higher Category Theory Internal to an Infinity Topos\nby S. W olf (Universität Regensburg) as part of ItaCa Fest 2024\n\n\nAbstract\nTh e goal of this talk will be to give a brief introduction to the theory of higher categories internal to an infinity-topos\, developed in joint work with Louis Martini. I will also indicate why such a theory is useful to ge t a better understanding of the geometry of infinity topoi. If time permit s\, I will conclude by explaining how one can use this language to give a characterization of proper morphism of infinity topoi in the sense of Luri e.\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2024/15/ END:VEVENT BEGIN:VEVENT SUMMARY:L. Spada (Università degli studi di Salerno) DTSTART:20240605T162000Z DTEND:20240605T170000Z DTSTAMP:20260422T225843Z UID:ItaCa-Fest-2024/16 DESCRIPTION:Title: 2-Weil 2-rigs\nby L. Spada (Università degli studi di Salern o) as part of ItaCa Fest 2024\n\n\nAbstract\nAmong commutative unital semi rings (rigs\, for short)\, let us call 2-Weil the ones that have a unique homomorphism into the distributive lattice 2. As 2 is the initial algebra in the category of additively idempotent rigs (2-rigs\, for short)\, 2-Wei l 2-rigs can be thought of as coordinate algebras of spaces with a single point. I will show how to characterize 2-Weil rigs as those that have uni que saturated prime ideal and will provide an axiomatization thereof in ge ometric logic. Further we will see that the category of 2-Weil 2-rigs is a co-reflective full subcategory of the category of 2-rigs.\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2024/16/ END:VEVENT BEGIN:VEVENT SUMMARY:G. Leoncini (Masaryk University / Università degli studi di Milan o) DTSTART:20241120T144000Z DTEND:20241120T152000Z DTSTAMP:20260422T225843Z UID:ItaCa-Fest-2024/17 DESCRIPTION:Title: Enriched Homotopy Cocompletions\nby G. Leoncini (Masaryk Univ ersity / Università degli studi di Milano) as part of ItaCa Fest 2024\n\n \nAbstract\nStarting from a 1-categorical base V which is not assumed endo wed with a choice of model structure (or any kind of homotopical structure )\, we propose a definition of homotopy colimits enriched in V in such a w ay that: (i) for V = Set\, we retrieve the classical theory of homotopy co limits\, and (ii) restricting to isomorphisms as weak equivalences\, we re trieve ordinary and enriched 1-colimits. We construct the free homotopy V- cocompletion of a small V-category in such a way that it satisfies the exp ected universal property. Over the base V = Set\, we retrieve Dugger’s c onstruction of the universal model category on a small category C. We inte rpret the homotopy V-enriched cocompletion of a point as the analogue of h omotopy theory of spaces in the enriched context. We compare our approach with some previous definitions of enriched homotopy colimits\, such as tho se given by Shulman\, Lack & Rosicky\, and Vokrinek\, and we show that\, w hen the latter are defined and well behaved\, they can be retrieved within our framework\, up to Quillen homotopy.\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2024/17/ END:VEVENT BEGIN:VEVENT SUMMARY:I. Di Liberti (Göteborgs universitet) DTSTART:20241120T152000Z DTEND:20241120T160000Z DTSTAMP:20260422T225843Z UID:ItaCa-Fest-2024/18 DESCRIPTION:Title: Taking ItaCa seriously\nby I. Di Liberti (Göteborgs universi tet) as part of ItaCa Fest 2024\n\n\nAbstract\nThis talk is a short presen tation of the ItaCa's historical progression\, its most important mileston es and its possible future perspectives.\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2024/18/ END:VEVENT END:VCALENDAR