BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Morgan Rogers (Università degli Studi dell'Insubria) DTSTART:20210209T141500Z DTEND:20210209T151500Z DTSTAMP:20260404T111244Z UID:CategoryTheory/1 DESCRIPTION:Title: Toposes of Topological Monoid Actions\nby Morgan Rogers (Università degli Studi dell'Insubria) as part of Cambridge Category Theo ry Seminar\n\n\nAbstract\nIt is well-known that\, for a topological group G\, the category Cont(G) of continuous actions of that\ngroup on Sets (vie wed as discrete spaces) is a topos. A similar proof works for topological monoids. Some follow-up\nquestions we tackle in this talk are:\nWhat prope rties do these toposes have?\nHow can we characterise them?\nWhat informat ion about a topological monoid M can we recover from Cont(M)?\nWhich topol ogical monoids are "good" representatives for such toposes?\n LOCATION:https://stable.researchseminars.org/talk/CategoryTheory/1/ END:VEVENT BEGIN:VEVENT SUMMARY:David Blázquez-Sanz (Universidad Nacional de Colombia) DTSTART:20210216T161500Z DTEND:20210216T171500Z DTSTAMP:20260404T111244Z UID:CategoryTheory/2 DESCRIPTION:Title: On the categorical structure behind Galois theories\nby David Blázquez-Sanz (Universidad Nacional de Colombia) as part of Cambrid ge Category Theory Seminar\n\n\nAbstract\nMost realizations of Galois theo ry rely on a set theoretical Galois group acting by automorphisms of an ob ject in a category.\nIn this talk we will discuss how\, if we ask the Galo is group to be a group object in the same category that the object in ques tion\,\nthen many different incarnations of Galois theory\, including clas sical\, Hopf-Galois\, differential\, and Galois theory adapt to the same\n categorical framework. We will also see that the realization of such theor y in the category of smooth bundles corresponds to some extension\nof the theory of principal connections in principal bundles. This talk is based o n the article "A simplified categorical approach to several\nGalois theori es" in collaboration with C. A. Marín-Arango y J. F. Ruiz.Castrillon.\n LOCATION:https://stable.researchseminars.org/talk/CategoryTheory/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Luca Reggio (University of Oxford) DTSTART:20210309T141500Z DTEND:20210309T151500Z DTSTAMP:20260404T111244Z UID:CategoryTheory/3 DESCRIPTION:Title: A characterisation of the category of compact Hausdorff spac es\nby Luca Reggio (University of Oxford) as part of Cambridge Categor y Theory Seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/CategoryTheory/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Davide Trotta (University of Pisa) DTSTART:20210511T151500Z DTEND:20210511T161500Z DTSTAMP:20260404T111244Z UID:CategoryTheory/4 DESCRIPTION:Title: The Gödel fibration\nby Davide Trotta (University of Pi sa) as part of Cambridge Category Theory Seminar\n\n\nAbstract\nIn this ta lk\, I will introduce the notion of Gödel fibration\, which is a fibratio n categorically embodying both the logical principles of traditional Skole mization and the existence of a prenex normal form presentation for every formula\, and I will explain how this notion is related to the Dialectica construction. In particular\, building up from Hofstra’s earlier fibrati onal characterization of de Paiva’s categorical Dialectica construction\ , I will show that a fibration is an instance of the Dialectica constructi on if and only if it is a Gödel fibration. This result establishes an int rinsic presentation of the Dialectica fibration\, contributing to the unde rstanding of the Dialectica construction itself and of its properties from a logical perspective. (Joint work with Matteo Spadetto and Valeria de Pa iva)\n LOCATION:https://stable.researchseminars.org/talk/CategoryTheory/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Martti Karvonen (University of Ottawa) DTSTART:20210525T151500Z DTEND:20210525T161500Z DTSTAMP:20260404T111244Z UID:CategoryTheory/5 DESCRIPTION:Title: Categorical composable cryptography\nby Martti Karvonen (University of Ottawa) as part of Cambridge Category Theory Seminar\n\n\nA bstract\nWe formalize the simulation paradigm of cryptography in terms of category theory\, resulting in an abstract model of composable security de finitions. We begin by recalling some background on cryptography and (cate gorical) resource theories. After this\, we explain the framework itself\, defined in terms of abstract attack model on a symmetric monoidal categor y\, and show that protocols secure against attacks form a symmetric monoid al category. We then use string diagrams to rederive no-go results concern ing the limits of bipartite\, ruling out e.g. composable commitments. Time permitting\, we discuss extensions of the framework that allow us to inco rporate computational security and set-up assumptions into the model.\n LOCATION:https://stable.researchseminars.org/talk/CategoryTheory/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Valeria de Paiva (Topos Institute) DTSTART:20210601T151500Z DTEND:20210601T161500Z DTSTAMP:20260404T111244Z UID:CategoryTheory/6 DESCRIPTION:Title: Categorical Models of Explicit Substitutions\nby Valeria de Paiva (Topos Institute) as part of Cambridge Category Theory Seminar\n \n\nAbstract\nThe advantages of functional programming are well-known: pro grams are easier to write\, understand and verify than their imperative co unterparts. However\, functional languages tend to be more memory intensiv e and these problems have hindered their wider use in industry. The xSLAM project tried to address these issues by using explicit substitutions to c onstruct and implement more efficient abstract machines. In this work we p rovide categorical models for the calculi of explicit substitutions (linea r and cartesian) that we are interested in.\n\nIndexed categories provide models of cartesian calculi of explicit substitutions. However\, these str uctures are inherently non-linear and hence cannot be used to model linear calculi of explicit substitutions. This work replaces indexed categories with pre-sheaves\, thus providing a categorical semantics covering both th e linear and cartesian cases. We justify our models by proving soundness a nd completeness results. Then we speculate on why there are not many model s around\, given the large number of calculi discussed in the community.\n LOCATION:https://stable.researchseminars.org/talk/CategoryTheory/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Richard Garner (Macquarie University) DTSTART:20210608T090000Z DTEND:20210608T101500Z DTSTAMP:20260404T111244Z UID:CategoryTheory/7 DESCRIPTION:Title: Cartesian differential categories as skew enriched categorie s\nby Richard Garner (Macquarie University) as part of Cambridge Categ ory Theory Seminar\n\n\nAbstract\nCartesian differential categories are an abstraction of the category of smooth maps between Euclidean spaces. Thei r main feature is an operator assigning to each map f:A -> B another map D f: A*A --> B called the differential of f\, subject to a list of axioms.\n \nIn this talk\, we explain the slightly surprising fact that cartesian di fferential categories are actually a kind of enriched category. The enrich ment base is the category of k-vector spaces\, but the monoidal structure is not the usual one\, but rather a skew-monoidal warping of it with respe ct to a monoidal comonad. The comonad at issue is not ad hoc\, but in fact the initial one imbuing k-vector spaces with the structure of a model of intuitionistic differential linear logic.\n\nThis is a report on joint wor k with JS Lemay.\n LOCATION:https://stable.researchseminars.org/talk/CategoryTheory/7/ END:VEVENT END:VCALENDAR