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BEGIN:VEVENT
SUMMARY:tslil clingman (Johns Hopkins University)
DTSTART;VALUE=DATE-TIME:20200916T210000Z
DTEND;VALUE=DATE-TIME:20200916T230000Z
DTSTAMP;VALUE=DATE-TIME:20240715T171809Z
UID:blue-jay-cat/1
DESCRIPTION:Title: BI DOUBLing categories we'll see / MULTIple morphisms acting weakly /
Two out of the four / Have laws rather poor / But the last is coherent VI
RTUALLY!\nby tslil clingman (Johns Hopkins University) as part of John
s Hopkins Category Theory Virtual Seminar\n\n\nAbstract\nAlthough 1-dimens
ional categories of various flavours are sufficient as\na universe of disc
ourse for many applications\, the theory of categories\nthemselves only tr
uly reveals itself in dimension 2. For this reason\,\nand for other natura
lly occurring motivating examples\, it is of use to\nmake rigorous and stu
dy various notions of 2-dimensional category.\n\nOf particular interest is
the ability of notions of 2-dimensional\ncategories to introduce "weaknes
s". Lifted from the confines of a\nsingle dimension we are now free to ask
for\, and study examples where\,\ncomposition of 1-dimensional morphisms
in a 2-dimensional category is no\nlonger strictly associative. Moreover\,
morphisms between 2-dimensional\ncategories themselves are now free to ob
ey functoriality to varying degrees.\n\nThe talk will take the form of a h
igh-level overview of the definitions\,\nexamples\, motivations for\, and
early theory of bi-categories\,\nmulticategories\, pseudo-double categorie
s and virtual double categories.\nThese definitions will be compared\, 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 that\, wh
en composition\nis defined by a universal property\, the complex laws and
theorems of\nnon-strict composition are automatic and functoriality is the
natural\nresult of the graded preservation of universality.\n\nPrerequisi
tes:\n\n- limits in a category\, especially products and pullbacks\n\n- mo
noidal categories\, and strict/strong/lax monoidal functors\n\n- the 2-cat
egory Cat of categories\, functors\, and natural transformations\n\nSugges
ted background: \n\nWe will find motivation in theory of pro-functors\nand
their composites\, as well as the theory of bi-modules over rings and\nth
eir tensors.\n
LOCATION:https://researchseminars.org/talk/blue-jay-cat/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Jaz Myers (Johns Hopkins University)
DTSTART;VALUE=DATE-TIME:20200923T210000Z
DTEND;VALUE=DATE-TIME:20200923T230000Z
DTSTAMP;VALUE=DATE-TIME:20240715T171809Z
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\, Generalized Logi
c\, and Closed Categories\, Lawvere notes that not only are the objects of
interest in mathematics organized into categories\, they often are catego
ries (of some flavor) in their own right. There are many different flavors
of category — enriched\, internal\, and stranger — each of which have
their own category theory. But just as there are many concepts throughout
mathematics which are unified by their expression in the algebra of compo
sition of maps\, there are many concepts in category theory which are unif
ied by their expression in the algebra of composition of natural transform
ations between bimodules. This algebra of natural transformations between
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 equipment.\n
LOCATION:https://researchseminars.org/talk/blue-jay-cat/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anthony Agwu (Johns Hopkins University)
DTSTART;VALUE=DATE-TIME:20201007T210000Z
DTEND;VALUE=DATE-TIME:20201007T230000Z
DTSTAMP;VALUE=DATE-TIME:20240715T171809Z
UID:blue-jay-cat/3
DESCRIPTION:Title: Partial maps and PCAs in categories\nby Anthony Agwu (Johns Hopki
ns University) as part of Johns Hopkins Category Theory Virtual Seminar\n\
n\nAbstract\nThis talk will give a brief introduction to restriction categ
ories and Turing categories\, including their motivations which relate to
partial maps and partial combinatory algebras (PCAs). First we will talk a
bout restriction categories where we'll introduce notions such as restrict
ion idempotents and ways they can be split. We'll then talk about how to h
andle products within restriction categories. After this\, we'll introduce
Turing categories and describe in depth their relationship with partial c
ombinatory algebras.\n
LOCATION:https://researchseminars.org/talk/blue-jay-cat/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Campbell (Johns Hopkins University)
DTSTART;VALUE=DATE-TIME:20201028T210000Z
DTEND;VALUE=DATE-TIME:20201028T230000Z
DTSTAMP;VALUE=DATE-TIME:20240715T171809Z
UID:blue-jay-cat/4
DESCRIPTION:Title: Quillen model structures in 2-category theory\nby Alexander Campb
ell (Johns Hopkins University) as part of Johns Hopkins Category Theory Vi
rtual 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-categ
ory theory.\n
LOCATION:https://researchseminars.org/talk/blue-jay-cat/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:tslil clingman (Johns Hopkins University)
DTSTART;VALUE=DATE-TIME:20201014T210000Z
DTEND;VALUE=DATE-TIME:20201014T230000Z
DTSTAMP;VALUE=DATE-TIME:20240715T171809Z
UID:blue-jay-cat/5
DESCRIPTION:Title: 2-lessons from Australian category theory: mates and doctrinal adjunc
tion\nby tslil clingman (Johns Hopkins University) as part of Johns Ho
pkins Category Theory Virtual Seminar\n\n\nAbstract\nPart of the lesson of
category theory is that adjunctions permeate\nmathematics at almost all l
evels\, from logic and topology to algebra and\nlanguage grammar. The cate
gorical method\, however\, teaches us that\nunderstanding is obtained by c
ollecting our objects of interest into a\ncategory and studying their stru
cture -- as given by their morphisms --\nen masse. What then\, on this vie
w\, is the structure supported by the\ncategory whose /objects/ are adjunc
tions? What is an appropriate notion\nof morphism here?\n\nIn this talk we
will begin to answer this question in greater (but not\ngreatest) general
ity by extracting\, from any 2-category\, at first a\ncategory and then la
ter double categories whose objects (and later\npro-arrows) are adjunction
s. This will allow us to see how morphisms\nbetween left adjoints correspo
nd to morphisms between right adjoints\,\nthe ``mate correspondence''. The
n\, in the double-categorical context\, we\nwill realise mates as a /very/
natural isomorphism between certain\ndouble functors. We will exploit thi
s naturality to give a theorem about\nthe transfer of all propositions and
structures on left adjoints\nexpressible in a certain language\, to corre
sponding propositions and\nstructures on their right adjoints. That is\, w
e will aim to make\nrigorous Leinster's view that ``all imaginable stateme
nts about mates\nare true.''\n\nWe will find applications of our theory of
mates in re-proving some of\nthe early theorems of adjunctions and\, if t
ime and interest permits\, to\nthe celebrated ``Doctrinal Adjunction'' res
ult 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 consequence\, i
n an adjunction of\nmonoidal categories the left adjoint is oplax-monoidal
iff. the right\nadjoint is lax-monoidal.\n\nPre-requisites:\n\n- Adjuncti
ons (equational definition in Cat)\n\n- 2-categories\, 2-functors (definit
ions and Cat as an example)\n\n- double categories\, double functors (defi
nitions)\n\nInessential but suggested:\n\n- horizontal and vertical double
-natural transformations\n
LOCATION:https://researchseminars.org/talk/blue-jay-cat/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Fuentes-Keuthan (Johns Hopkins University)
DTSTART;VALUE=DATE-TIME:20201111T220000Z
DTEND;VALUE=DATE-TIME:20201112T000000Z
DTSTAMP;VALUE=DATE-TIME:20240715T171809Z
UID:blue-jay-cat/6
DESCRIPTION:Title: Unstraightened Algebra\nby Daniel Fuentes-Keuthan (Johns Hopkins
University) as part of Johns Hopkins Category Theory Virtual Seminar\n\n\n
Abstract\nNaive attempts to define homotopy coherent algebraic structures
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 ensu
re homotopical associativity. We study monoids via simplicial objects know
n as their bar constructions\, and show how weakening some of the assumpti
ons in the bar construction leads to the appropriate homotopy coherent str
ucture. This way of thinking applies readily to category theory\, where a
strict monoidal category is a strict monoid object\, and a monoidal catego
ry is a homotopy coherent monoid. In the case of categories we can go a st
ep further and associate a cocartesian fibration to a monoidal category's
bar construction via the Grothendieck construction. This allows us to reca
st the theory of monoidal categories\, lax monoidal functions\, and algebr
as over operads in terms of cocartesian fibrations over the simplex catego
ry. While packaging coherence data this way might seem like overkill\, sin
ce normal category theory is naturally only 2-dimensional\, it gives a way
to extend the theory of monoidal structures to the infinity category worl
d. Indeed this is the approach taken by Lurie in Higher Algebra to define
and study infinity operads and monoidal infinity categories.\n
LOCATION:https://researchseminars.org/talk/blue-jay-cat/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Jaz Myers (Johns Hopkins University)
DTSTART;VALUE=DATE-TIME:20201118T220000Z
DTEND;VALUE=DATE-TIME:20201119T000000Z
DTSTAMP;VALUE=DATE-TIME:20240715T171809Z
UID:blue-jay-cat/7
DESCRIPTION:Title: Comparing left and right derived functors with double categories\
nby David Jaz Myers (Johns Hopkins University) as part of Johns Hopkins Ca
tegory Theory Virtual Seminar\n\n\nAbstract\nFor functors between abelian
categories which fail to be exact\, there are left and right derived funct
ors which encode obstructions to exactness on a homological level. These d
erived functors are quite readily described using the language of model ca
tegories applied to categories of chain complexes. In this talk\, we will
explore the double functoriality of taking left and right derived functors
\, and use this to give a derived version of the projection formula for ba
se change along a proper map between locally compact Hausdorff spaces.\n
LOCATION:https://researchseminars.org/talk/blue-jay-cat/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Jaz Myers (Johns Hopkins University)
DTSTART;VALUE=DATE-TIME:20201209T220000Z
DTEND;VALUE=DATE-TIME:20201210T000000Z
DTSTAMP;VALUE=DATE-TIME:20240715T171809Z
UID:blue-jay-cat/9
DESCRIPTION:Title: A cup of HoTT cocoa\nby David Jaz Myers (Johns Hopkins University
) as part of Johns Hopkins Category Theory Virtual Seminar\n\n\nAbstract\n
Join me around the fire with a cup of HoTT cocoa for orbifold storytime. I
n homotopy type theory\, we may define a group as the type of self-identif
ications --- or symmetries --- of an object. But HoTT offers a radical cha
nge in perspective on groups: instead of working with the symmetries direc
tly\, we work with the images of an object --- those things which are iden
tifiable with it (though not in any canonical way). We'll play around with
this viewpoint and see how to represent groups and actions via images. Th
en we'll see how to define some simple orbifolds in HoTT\, and learn that
orbifolds have points just like manifolds do\, and that it can be very fun
to work with them. Along the way I will drop some puzzles to chew on\, wh
ich we will share our favorite solutions to at the end.\n
LOCATION:https://researchseminars.org/talk/blue-jay-cat/9/
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