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SUMMARY:Morgan Rogers (Università degli Studi dell'Insubria)
DTSTART;VALUE=DATE-TIME:20210209T141500Z
DTEND;VALUE=DATE-TIME:20210209T151500Z
DTSTAMP;VALUE=DATE-TIME:20240624T062519Z
UID:CategoryTheory/1
DESCRIPTION:Title: Toposes of Topological Monoid Actions\nby Morgan Rogers (Univer
sità degli Studi dell'Insubria) as part of Cambridge Category Theory Semi
nar\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 (viewed as
discrete spaces) is a topos. A similar proof works for topological monoids
. Some follow-up\nquestions we tackle in this talk are:\nWhat properties d
o these toposes have?\nHow can we characterise them?\nWhat information abo
ut a topological monoid M can we recover from Cont(M)?\nWhich topological
monoids are "good" representatives for such toposes?\n
LOCATION:https://researchseminars.org/talk/CategoryTheory/1/
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SUMMARY:David Blázquez-Sanz (Universidad Nacional de Colombia)
DTSTART;VALUE=DATE-TIME:20210216T161500Z
DTEND;VALUE=DATE-TIME:20210216T171500Z
DTSTAMP;VALUE=DATE-TIME:20240624T062519Z
UID:CategoryTheory/2
DESCRIPTION:Title: On the categorical structure behind Galois theories\nby David B
lázquez-Sanz (Universidad Nacional de Colombia) as part of Cambridge Cate
gory Theory Seminar\n\n\nAbstract\nMost realizations of Galois theory rely
on a set theoretical Galois group acting by automorphisms of an object in
a category.\nIn this talk we will discuss how\, if we ask the Galois grou
p to be a group object in the same category that the object in question\,\
nthen many different incarnations of Galois theory\, including classical\,
Hopf-Galois\, differential\, and Galois theory adapt to the same\ncategor
ical framework. We will also see that the realization of such theory in th
e category of smooth bundles corresponds to some extension\nof the theory
of principal connections in principal bundles. This talk is based on the a
rticle "A simplified categorical approach to several\nGalois theories" in
collaboration with C. A. Marín-Arango y J. F. Ruiz.Castrillon.\n
LOCATION:https://researchseminars.org/talk/CategoryTheory/2/
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BEGIN:VEVENT
SUMMARY:Luca Reggio (University of Oxford)
DTSTART;VALUE=DATE-TIME:20210309T141500Z
DTEND;VALUE=DATE-TIME:20210309T151500Z
DTSTAMP;VALUE=DATE-TIME:20240624T062519Z
UID:CategoryTheory/3
DESCRIPTION:Title: A characterisation of the category of compact Hausdorff spaces\
nby Luca Reggio (University of Oxford) as part of Cambridge Category Theor
y Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CategoryTheory/3/
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SUMMARY:Davide Trotta (University of Pisa)
DTSTART;VALUE=DATE-TIME:20210511T151500Z
DTEND;VALUE=DATE-TIME:20210511T161500Z
DTSTAMP;VALUE=DATE-TIME:20240624T062519Z
UID:CategoryTheory/4
DESCRIPTION:Title: The Gödel fibration\nby Davide Trotta (University of Pisa) as
part of Cambridge Category Theory Seminar\n\n\nAbstract\nIn this talk\, I
will introduce the notion of Gödel fibration\, which is a fibration categ
orically embodying both the logical principles of traditional Skolemizatio
n and the existence of a prenex normal form presentation for every formula
\, and I will explain how this notion is related to the Dialectica constru
ction. In particular\, building up from Hofstra’s earlier fibrational ch
aracterization of de Paiva’s categorical Dialectica construction\, I wil
l show that a fibration is an instance of the Dialectica construction if a
nd only if it is a Gödel fibration. This result establishes an intrinsic
presentation of the Dialectica fibration\, contributing to the understandi
ng of the Dialectica construction itself and of its properties from a logi
cal perspective. (Joint work with Matteo Spadetto and Valeria de Paiva)\n
LOCATION:https://researchseminars.org/talk/CategoryTheory/4/
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BEGIN:VEVENT
SUMMARY:Martti Karvonen (University of Ottawa)
DTSTART;VALUE=DATE-TIME:20210525T151500Z
DTEND;VALUE=DATE-TIME:20210525T161500Z
DTSTAMP;VALUE=DATE-TIME:20240624T062519Z
UID:CategoryTheory/5
DESCRIPTION:Title: Categorical composable cryptography\nby Martti Karvonen (Univer
sity of Ottawa) as part of Cambridge Category Theory Seminar\n\n\nAbstract
\nWe formalize the simulation paradigm of cryptography in terms of categor
y theory\, resulting in an abstract model of composable security definitio
ns. We begin by recalling some background on cryptography and (categorical
) resource theories. After this\, we explain the framework itself\, define
d in terms of abstract attack model on a symmetric monoidal category\, and
show that protocols secure against attacks form a symmetric monoidal cate
gory. We then use string diagrams to rederive no-go results concerning the
limits of bipartite\, ruling out e.g. composable commitments. Time permit
ting\, we discuss extensions of the framework that allow us to incorporate
computational security and set-up assumptions into the model.\n
LOCATION:https://researchseminars.org/talk/CategoryTheory/5/
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BEGIN:VEVENT
SUMMARY:Valeria de Paiva (Topos Institute)
DTSTART;VALUE=DATE-TIME:20210601T151500Z
DTEND;VALUE=DATE-TIME:20210601T161500Z
DTSTAMP;VALUE=DATE-TIME:20240624T062519Z
UID:CategoryTheory/6
DESCRIPTION:Title: Categorical Models of Explicit Substitutions\nby Valeria de Pai
va (Topos Institute) as part of Cambridge Category Theory Seminar\n\n\nAbs
tract\nThe advantages of functional programming are well-known: programs a
re easier to write\, understand and verify than their imperative counterpa
rts. However\, functional languages tend to be more memory intensive and t
hese problems have hindered their wider use in industry. The xSLAM project
tried to address these issues by using explicit substitutions to construc
t and implement more efficient abstract machines. In this work we provide
categorical models for the calculi of explicit substitutions (linear and c
artesian) that we are interested in.\n\nIndexed categories provide models
of cartesian calculi of explicit substitutions. However\, these structures
are inherently non-linear and hence cannot be used to model linear calcul
i of explicit substitutions. This work replaces indexed categories with pr
e-sheaves\, thus providing a categorical semantics covering both the linea
r and cartesian cases. We justify our models by proving soundness and comp
leteness results. Then we speculate on why there are not many models aroun
d\, given the large number of calculi discussed in the community.\n
LOCATION:https://researchseminars.org/talk/CategoryTheory/6/
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SUMMARY:Richard Garner (Macquarie University)
DTSTART;VALUE=DATE-TIME:20210608T090000Z
DTEND;VALUE=DATE-TIME:20210608T101500Z
DTSTAMP;VALUE=DATE-TIME:20240624T062519Z
UID:CategoryTheory/7
DESCRIPTION:Title: Cartesian differential categories as skew enriched categories\n
by Richard Garner (Macquarie University) as part of Cambridge Category The
ory Seminar\n\n\nAbstract\nCartesian differential categories are an abstra
ction of the category of smooth maps between Euclidean spaces. Their main
feature is an operator assigning to each map f:A -> B another map Df: A*A
--> B called the differential of f\, subject to a list of axioms.\n\nIn th
is talk\, we explain the slightly surprising fact that cartesian different
ial categories are actually a kind of enriched category. The enrichment ba
se 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 respect to a
monoidal comonad. The comonad at issue is not ad hoc\, but in fact the in
itial one imbuing k-vector spaces with the structure of a model of intuiti
onistic differential linear logic.\n\nThis is a report on joint work with
JS Lemay.\n
LOCATION:https://researchseminars.org/talk/CategoryTheory/7/
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