BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:A. Lorenzin DTSTART:20220420T130000Z DTEND:20220420T140000Z DTSTAMP:20260422T225842Z UID:ItaCa-Fest-2022/1 DESCRIPTION:Title: Formality and strongly unique enhancements\nby A. Lorenzin as part of ItaCa Fest 2022\n\n\nAbstract\nFormality and strongly unique enhan cements\nAbstract: Inspired by the intrinsic formality of graded algebras\ , we give a characterization of strongly unique DG-enhancements for a larg e class of algebraic triangulated categories\, linear over a commutative r ing. We will discuss applications to bounded derived categories and bounde d homotopy categories of complexes. For the sake of an example\, the bound ed derived category of finitely generated abelian groups has a strongly un ique enhancement.\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2022/1/ END:VEVENT BEGIN:VEVENT SUMMARY:M. Karvonen DTSTART:20220420T140000Z DTEND:20220420T150000Z DTSTAMP:20260422T225842Z UID:ItaCa-Fest-2022/2 DESCRIPTION:Title: Inner automorphisms as 2-cells\nby M. Karvonen as part of ItaC a Fest 2022\n\n\nAbstract\nThinking of groups as one-object categories mak es the category of groups naturally into a 2-category. We observe that a s imilar construction works for any category: a 2-cell f->g is given by an i nner automorphism of the codomain that takes f to g\, where inner automomo rphisms are defined in general using isotropy groups. We will explore the behavior of limits and colimits in the resulting 2-category: when the unde rlying category is cocomplete\, the resulting 2-category has coequalizers iff the isotropy functor is representable - in the case of groups\, this a mounts to deducing the existence of HNN-extensions from the representabili ty of id:Grp->Grp. Under reasonable conditions\, limits and connected coli mits in the underlying category are 2-categorical limits/colimits in the r esulting 2-category. However\, many other 2-dimensional limits and colimit s fail to exist\, unless the underlying category has only trivial inner au tomorphisms.\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2022/2/ END:VEVENT BEGIN:VEVENT SUMMARY:G. Coraglia DTSTART:20220519T130000Z DTEND:20220519T140000Z DTSTAMP:20260422T225842Z UID:ItaCa-Fest-2022/3 DESCRIPTION:Title: Comonads for dependent types\nby G. Coraglia as part of ItaCa Fest 2022\n\n\nAbstract\nIn exploring the relation between a classical mod el of dependent types (comprehension categories) and a new one (judgementa l dtts) we pin-point the comonadic behaviour of weakening and contraction. We describe three different 2-categories and show that they are 2-equival ent\, then proceed to analyze the benefits of each of the three. The fact that one can precisely relate such different perspectives allows\, for exa mple\, for a swift and cleaner treatment of type constructors: we show how certain categorical models for dependent types come inherently equipped w ith some due to the choices one makes in introducing tools to interpret co ntext extension.\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2022/3/ END:VEVENT BEGIN:VEVENT SUMMARY:J. Kock DTSTART:20220519T140000Z DTEND:20220519T150000Z DTSTAMP:20260422T225842Z UID:ItaCa-Fest-2022/4 DESCRIPTION:Title: Decomposition spaces\, right fibrations\, and edgewise subdivision \nby J. Kock as part of ItaCa Fest 2022\n\n\nAbstract\nDecomposition s paces are simplicial infinity-groupoids subject to an exactness condition weaker than the Segal condition. Where the Segal condition expresses compo sition\, the weak condition expresses decomposition. The motivation for st udying decomposition spaces is that they have incidence coalgebras and Mö bius inversion. The most important class of simplicial maps for decomposit ion spaces are the CULF maps (standing for ‘conservative’ and ‘uniqu e-lifting-of-factorisation’)\, first studied by Lawvere\; they induce co algebra homomorphisms. The theorem I want to arrive at in the talk says th at the infinity-category of (Rezk-complete) decomposition spaces and CULF maps is locally an infinity-topos. More precisely for each (Rezk-complete) decomposition space D\, the slice infinity-category Decomp/D is equivalen t to PrSh(Sd(D))\, the infinity-topos of presheaves on the edgewise subdiv ision of D. Most of the talk will be spent on explaining preliminaries\, t hough.\n\nThis is joint work with Philip Hackney.\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2022/4/ END:VEVENT BEGIN:VEVENT SUMMARY:F. Bonchi DTSTART:20220628T130000Z DTEND:20220628T140000Z DTSTAMP:20260422T225842Z UID:ItaCa-Fest-2022/5 DESCRIPTION:Title: Deconstructing Tarski’s calculus of relations with Tape diagrams \nby F. Bonchi as part of ItaCa Fest 2022\n\n\nAbstract\nThe calculus of (binary) relations has been introduced by Tarski as a variable-free alt ernative to first order logic. In this talk we introduce tape diagrams\, a graphical language for expressing arrows of arbitrary finite biproduct ri g categories\, and we show how the calculus of relation can be encoded wit hin tape diagrams.\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2022/5/ END:VEVENT BEGIN:VEVENT SUMMARY:I. Blenchschmidt DTSTART:20220628T140000Z DTEND:20220628T150000Z DTSTAMP:20260422T225842Z UID:ItaCa-Fest-2022/6 DESCRIPTION:Title: Reifying dynamical algebra: Traveling the mathematical multiverse to apply tools for the countable also to the uncountable\nby I. Blench schmidt as part of ItaCa Fest 2022\n\n\nAbstract\nCommutative algebra abou nds with proofs which are quite elegant and at the same time quite abstrac t. Even for concrete statements\, proofs often appeal to transfinite metho ds like the axiom of choice or the law of excluded middle. Following Hilbe rt’s call\, we should work to elucidate how these abstract proofs can be recast in more concrete\, computational terms\, regarding abstract proofs as intriguing guiding templates for formulating concrete proofs and regar ding objects concocted by Zorn’s lemma such as maximal ideals as conveni ent fictions. One such technique for making computational sense of abstrac t proofs is dynamical algebra\, going back to the work of Dominique Duval and her coauthors in the 1980’s. The talk will first present the basic s tory of dynamical algebra with an illustrative example. Then we will repor t on joint work with Peter Schuster how to reify dynamical algebra using f ormal metatheorems of categorical logic\, supplying a firm foundation to d ynamical algebra\, complementing previous approaches. A particular feature of our approach is that we apply a construction devised by Berardi and Va lentini for the special case of countable rings\, which indeed fundamental ly requires the countability assumption\, by a logical sleight of hand by Joyal and Tierney to arbitrary rings. This trick is applicable quite gener ally which is why we believe that it is of interest to a larger group of p eople. It is unlocked by categorical logic running on a certain fractal wi thout points\, the pointfree space of enumerations of a given set.\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2022/6/ END:VEVENT BEGIN:VEVENT SUMMARY:A. Cigoli DTSTART:20220920T130000Z DTEND:20220920T140000Z DTSTAMP:20260422T225842Z UID:ItaCa-Fest-2022/7 DESCRIPTION:Title: Groupal Pseudofunctors\nby A. Cigoli as part of ItaCa Fest 202 2\n\n\nAbstract\nLet B be an additive category and let Set denote the cate gory of sets. A finite product preserving functor F from B to Set necessar ily factors through the category Ab of abelian groups. This simple and imp ortant observation has no straightforward generalization when F and Set ar e replaced by a pseudo-functor and the 2-category Cat of categories\, resp ectively. The latter situation occurs precisely when B is the base categor y of an opfibration. In this talk\, we will focus on pseudo-functors corre sponding to cartesian monoidal opfibrations of codomain B. Among such\, we will eventually characterize\, in terms of oplax and lax monoidal structu re\, those factorizing through the bicategory of symmetric categorical gro ups. This is the case\, for example\, when the starting opfibration has gr oupoidal fibres. This is joint work with S. Mantovani and G. Metere.\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2022/7/ END:VEVENT BEGIN:VEVENT SUMMARY:L. Reggio DTSTART:20220920T140000Z DTEND:20220920T150000Z DTSTAMP:20260422T225842Z UID:ItaCa-Fest-2022/8 DESCRIPTION:Title: Arboreal categories and homomorphism preservation theorems\nby L. Reggio as part of ItaCa Fest 2022\n\n\nAbstract\nGame comonads\, intro duced by Abramsky\, Dawar et al. in 2017\, provide a categorical approach to (finite) model theory. In this framework one can capture\, in a purely syntax-free way\, various resource-sensitive logic fragments and correspon ding combinatorial parameters. After an introduction to game comonads\, I shall present an axiomatic framework which captures the essential common f eatures of these constructions. This is based on the notion of arboreal ca tegory\, in which every object is generated by its `paths’. I will then show how (resource-sensitive) homomorphism preservation theorems in logic can be recast and proved at this axiomatic level. This is joint work with Samson Abramsky.\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2022/8/ END:VEVENT BEGIN:VEVENT SUMMARY:M. Escardó DTSTART:20221018T130000Z DTEND:20221018T140000Z DTSTAMP:20260422T225842Z UID:ItaCa-Fest-2022/9 DESCRIPTION:Title: Compact totally separated types\nby M. Escardó as part of Ita Ca Fest 2022\n\n\nAbstract\nWe define notions of compactness and total sep aratedness for types corresponding to topological notions with the same na me. The objective is not to be faithful to topology\, but instead to get i nspiration from topology for obtaining surprising results in constructive mathematics.\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2022/9/ END:VEVENT BEGIN:VEVENT SUMMARY:M. Capucci DTSTART:20221018T140000Z DTEND:20221018T150000Z DTSTAMP:20260422T225842Z UID:ItaCa-Fest-2022/10 DESCRIPTION:Title: Triple categories of open cybernetic systems\nby M. Capucci a s part of ItaCa Fest 2022\n\n\nAbstract\nCategorical system theory (in the sense of Myers) is a double categorical yoga for describing the compositi onal structure of open dynamical systems. It unifies and improves on previ ous work on operadic notions of system theory\, and provides a strong conc eptual scaffolding for behavioral system theory. However\, some of the mos t interesting systems out there escape the simple model of dynamical syste ms. They are instead cybernetic systems\, or in other words\, controllable dynamical systems. Notable and motivating examples are strategic games an d machine learning models. In this talk I’m going to outline an upgrade of categorical system theory to deal with such systems by resorting to tri ple categories.\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2022/10/ END:VEVENT BEGIN:VEVENT SUMMARY:N. Di Vittorio DTSTART:20221122T083000Z DTEND:20221122T093000Z DTSTAMP:20260422T225842Z UID:ItaCa-Fest-2022/11 DESCRIPTION:Title: A gentle introduction to 2-derivators\nby N. Di Vittorio as p art of ItaCa Fest 2022\n\n\nAbstract\nDerivators originated in the 1980s f rom independent efforts by Grothendieck and Heller aimed at formalising ho motopy theory. They realised that the collection of homotopy categories of diagram categories retains enough information to capture homotopy limits and colimits using just old-fashioned category theory. Going one dimension up we could ask how much of $(\\infty\,1)$-category theory can be develop ed in this way. Progress in this direction has been done by Riehl and Veri ty in their work on $\\infty$-cosmoi by showing that similar ideas allow e ven for internalisation of adjunctions from 2-categorical data. In this ta lk I will explain to which extent the theory of derivators can be enhanced to a theory of $2$-derivators having $\\infty$-cosmology as a model.\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2022/11/ END:VEVENT BEGIN:VEVENT SUMMARY:G. Raptis DTSTART:20221122T093000Z DTEND:20221122T103000Z DTSTAMP:20260422T225842Z UID:ItaCa-Fest-2022/12 DESCRIPTION:Title: What is a stable n-category?\nby G. Raptis as part of ItaCa F est 2022\n\n\nAbstract\nTriangulated categories provide a convenient frame work for the study of derived functors in algebra and geometry. In most ca ses of interest\, triangulated structures can be enhanced to more highly s tructured objects with better properties. The search for appropriate enhan cements of triangulated categories has led to various foundational approac hes in stable homotopy theory. In the context of \\infty-categories (or qu asi-categories)\, this involves the notion of stable \\infty-category. Ind eed\, the homotopy 1-category of a stable \\infty-category is canonically triangulated. But what about n-categories for 1 < n < \\infty? Is there an appropriate notion of stable (or triangulated) category in the context of n-categories that interpolates between stable \\infty-categories and tria ngulated categories? The main examples should again be the homotopy n-cate gories of stable \\infty-categories. In this talk\, I will discuss the rel evant properties of higher homotopy categories leading to a notion of stab le n-category. If time permits\, I will also mention some uses of this not ion of stable n-category for (higher) Brown representability and algebraic K-theory.\n LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2022/12/ END:VEVENT END:VCALENDAR