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BEGIN:VEVENT
SUMMARY:tslil clingman (Johns Hopkins University)
DTSTART:20200916T210000Z
DTEND:20200916T230000Z
DTSTAMP:20260404T095716Z
UID:blue-jay-cat/1
DESCRIPTION:Title: BI DOUBLing categories we'll see / MULTIple morphisms acting w
eakly / Two out of the four / Have laws rather poor / But the last is cohe
rent VIRTUALLY!\nby tslil clingman (Johns Hopkins University) as part
of Johns Hopkins Category Theory Virtual Seminar\n\n\nAbstract\nAlthough 1
-dimensional categories of various flavours are sufficient as\na universe
of discourse for many applications\, the theory of categories\nthemselves
only truly reveals itself in dimension 2. For this reason\,\nand for other
naturally occurring motivating examples\, it is of use to\nmake rigorous
and study various notions of 2-dimensional category.\n\nOf particular inte
rest is the ability of notions of 2-dimensional\ncategories to introduce "
weakness". Lifted from the confines of a\nsingle dimension we are now free
to ask for\, and study examples where\,\ncomposition of 1-dimensional mor
phisms in a 2-dimensional category is no\nlonger strictly associative. Mor
eover\, morphisms between 2-dimensional\ncategories themselves are now fre
e to obey functoriality to varying degrees.\n\nThe talk will take the form
of a high-level overview of the definitions\,\nexamples\, motivations for
\, and early theory of bi-categories\,\nmulticategories\, pseudo-double ca
tegories and virtual double categories.\nThese definitions will be compare
d\, and each will be paired with an\naccompanying notions of morphisms of
varying strictness.\n\nThe goal of the talk is to advocate for the view th
at\, when composition\nis defined by a universal property\, the complex la
ws and theorems of\nnon-strict composition are automatic and functoriality
is the natural\nresult of the graded preservation of universality.\n\nPre
requisites:\n\n- limits in a category\, especially products and pullbacks\
n\n- monoidal categories\, and strict/strong/lax monoidal functors\n\n- th
e 2-category Cat of categories\, functors\, and natural transformations\n\
nSuggested background: \n\nWe will find motivation in theory of pro-functo
rs\nand their composites\, as well as the theory of bi-modules over rings
and\ntheir tensors.\n
LOCATION:https://stable.researchseminars.org/talk/blue-jay-cat/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Jaz Myers (Johns Hopkins University)
DTSTART:20200923T210000Z
DTEND:20200923T230000Z
DTSTAMP:20260404T095716Z
UID:blue-jay-cat/2
DESCRIPTION:Title: Getting equipped for formal category theory\nby David Jaz
Myers (Johns Hopkins University) as part of Johns Hopkins Category Theory
Virtual Seminar\n\n\nAbstract\nIn his 1973 paper Metric Spaces\, Generaliz
ed Logic\, and Closed Categories\, Lawvere notes that not only are the obj
ects of interest in mathematics organized into categories\, they often are
categories (of some flavor) in their own right. There are many different
flavors of category — enriched\, internal\, and stranger — each of whi
ch have their own category theory. But just as there are many concepts thr
oughout mathematics which are unified by their expression in the algebra o
f composition of maps\, there are many concepts in category theory which a
re unified by their expression in the algebra of composition of natural tr
ansformations between bimodules. This algebra of natural transformations b
etween bimodules is described by a virtual equipment. In this talk\, we'll
see a bit of what category theory looks like in a general virtual equipme
nt.\n
LOCATION:https://stable.researchseminars.org/talk/blue-jay-cat/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anthony Agwu (Johns Hopkins University)
DTSTART:20201007T210000Z
DTEND:20201007T230000Z
DTSTAMP:20260404T095716Z
UID:blue-jay-cat/3
DESCRIPTION:Title: Partial maps and PCAs in categories\nby Anthony Agwu (John
s Hopkins University) as part of Johns Hopkins Category Theory Virtual Sem
inar\n\n\nAbstract\nThis talk will give a brief introduction to restrictio
n categories and Turing categories\, including their motivations which rel
ate to partial maps and partial combinatory algebras (PCAs). First we will
talk about restriction categories where we'll introduce notions such as r
estriction idempotents and ways they can be split. We'll then talk about h
ow to handle products within restriction categories. After this\, we'll in
troduce Turing categories and describe in depth their relationship with pa
rtial combinatory algebras.\n
LOCATION:https://stable.researchseminars.org/talk/blue-jay-cat/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Campbell (Johns Hopkins University)
DTSTART:20201028T210000Z
DTEND:20201028T230000Z
DTSTAMP:20260404T095716Z
UID:blue-jay-cat/4
DESCRIPTION:Title: Quillen model structures in 2-category theory\nby Alexande
r Campbell (Johns Hopkins University) as part of Johns Hopkins Category Th
eory Virtual Seminar\n\n\nAbstract\nThe goal of this talk is to introduce
some of the basic concepts of model category theory from the point of view
of a 2-category theorist. All motivation and examples will be drawn from
2-category theory.\n
LOCATION:https://stable.researchseminars.org/talk/blue-jay-cat/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:tslil clingman (Johns Hopkins University)
DTSTART:20201014T210000Z
DTEND:20201014T230000Z
DTSTAMP:20260404T095716Z
UID:blue-jay-cat/5
DESCRIPTION:Title: 2-lessons from Australian category theory: mates and doctrinal
adjunction\nby tslil clingman (Johns Hopkins University) as part of J
ohns Hopkins Category Theory Virtual Seminar\n\n\nAbstract\nPart of the le
sson of category theory is that adjunctions permeate\nmathematics at almos
t all levels\, from logic and topology to algebra and\nlanguage grammar. T
he categorical method\, however\, teaches us that\nunderstanding is obtain
ed by collecting our objects of interest into a\ncategory and studying the
ir structure -- as given by their morphisms --\nen masse. What then\, on t
his view\, is the structure supported by the\ncategory whose /objects/ are
adjunctions? What is an appropriate notion\nof morphism here?\n\nIn this
talk we will begin to answer this question in greater (but not\ngreatest)
generality by extracting\, from any 2-category\, at first a\ncategory and
then later double categories whose objects (and later\npro-arrows) are adj
unctions. This will allow us to see how morphisms\nbetween left adjoints c
orrespond to morphisms between right adjoints\,\nthe ``mate correspondence
''. Then\, in the double-categorical context\, we\nwill realise mates as a
/very/ natural isomorphism between certain\ndouble functors. We will expl
oit this naturality to give a theorem about\nthe transfer of all propositi
ons and structures on left adjoints\nexpressible in a certain language\, t
o corresponding propositions and\nstructures on their right adjoints. That
is\, we will aim to make\nrigorous Leinster's view that ``all imaginable
statements about mates\nare true.''\n\nWe will find applications of our th
eory of mates in re-proving some of\nthe early theorems of adjunctions and
\, if time and interest permits\, to\nthe celebrated ``Doctrinal Adjunctio
n'' result of Kelly. The central\nresult of this paper relates adjunctions
of lax- and colax-morphisms of\n2-dimensional algebras for 2-dimensional
monads to adjunctions of the\nunderlying objects. As a particular conseque
nce\, in an adjunction of\nmonoidal categories the left adjoint is oplax-m
onoidal iff. the right\nadjoint is lax-monoidal.\n\nPre-requisites:\n\n- A
djunctions (equational definition in Cat)\n\n- 2-categories\, 2-functors (
definitions and Cat as an example)\n\n- double categories\, double functor
s (definitions)\n\nInessential but suggested:\n\n- horizontal and vertical
double-natural transformations\n
LOCATION:https://stable.researchseminars.org/talk/blue-jay-cat/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Fuentes-Keuthan (Johns Hopkins University)
DTSTART:20201111T220000Z
DTEND:20201112T000000Z
DTSTAMP:20260404T095716Z
UID:blue-jay-cat/6
DESCRIPTION:Title: Unstraightened Algebra\nby Daniel Fuentes-Keuthan (Johns H
opkins University) as part of Johns Hopkins Category Theory Virtual Semina
r\n\n\nAbstract\nNaive attempts to define homotopy coherent algebraic stru
ctures in topology lead to issues of book-keeping and the problem of data
versus structure as one must specify an infinite amount of coherence data
to ensure homotopical associativity. We study monoids via simplicial objec
ts known as their bar constructions\, and show how weakening some of the a
ssumptions in the bar construction leads to the appropriate homotopy coher
ent structure. This way of thinking applies readily to category theory\, w
here a strict monoidal category is a strict monoid object\, and a monoidal
category is a homotopy coherent monoid. In the case of categories we can
go a step further and associate a cocartesian fibration to a monoidal cate
gory's bar construction via the Grothendieck construction. This allows us
to recast the theory of monoidal categories\, lax monoidal functions\, and
algebras over operads in terms of cocartesian fibrations over the simplex
category. While packaging coherence data this way might seem like overkil
l\, since normal category theory is naturally only 2-dimensional\, it give
s a way to extend the theory of monoidal structures to the infinity catego
ry world. Indeed this is the approach taken by Lurie in Higher Algebra to
define and study infinity operads and monoidal infinity categories.\n
LOCATION:https://stable.researchseminars.org/talk/blue-jay-cat/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Jaz Myers (Johns Hopkins University)
DTSTART:20201118T220000Z
DTEND:20201119T000000Z
DTSTAMP:20260404T095716Z
UID:blue-jay-cat/7
DESCRIPTION:Title: Comparing left and right derived functors with double categori
es\nby David Jaz Myers (Johns Hopkins University) as part of Johns Hop
kins Category Theory Virtual Seminar\n\n\nAbstract\nFor functors between a
belian categories which fail to be exact\, there are left and right derive
d functors which encode obstructions to exactness on a homological level.
These derived functors are quite readily described using the language of m
odel categories applied to categories of chain complexes. In this talk\, w
e will explore the double functoriality of taking left and right derived f
unctors\, and use this to give a derived version of the projection formula
for base change along a proper map between locally compact Hausdorff spac
es.\n
LOCATION:https://stable.researchseminars.org/talk/blue-jay-cat/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Jaz Myers (Johns Hopkins University)
DTSTART:20201209T220000Z
DTEND:20201210T000000Z
DTSTAMP:20260404T095716Z
UID:blue-jay-cat/9
DESCRIPTION:Title: A cup of HoTT cocoa\nby David Jaz Myers (Johns Hopkins Uni
versity) as part of Johns Hopkins Category Theory Virtual Seminar\n\n\nAbs
tract\nJoin me around the fire with a cup of HoTT cocoa for orbifold story
time. In homotopy type theory\, we may define a group as the type of self-
identifications --- or symmetries --- of an object. But HoTT offers a radi
cal change in perspective on groups: instead of working with the symmetrie
s directly\, we work with the images of an object --- those things which a
re identifiable with it (though not in any canonical way). We'll play arou
nd with this viewpoint and see how to represent groups and actions via ima
ges. Then we'll see how to define some simple orbifolds in HoTT\, and lear
n that orbifolds have points just like manifolds do\, and that it can be v
ery fun to work with them. Along the way I will drop some puzzles to chew
on\, which we will share our favorite solutions to at the end.\n
LOCATION:https://stable.researchseminars.org/talk/blue-jay-cat/9/
END:VEVENT
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