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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:20201101T005605Z
UID:blue-jay-cat/1
DESCRIPTION:Title: BI DOUBLing categories we'll see / MULTIple morphisms a
cting weakly / Two out of the four / Have laws rather poor / But the last
is coherent VIRTUALLY!\nby tslil clingman (Johns Hopkins University) as pa
rt of Johns Hopkins Category Theory Virtual Seminar\n\n\nAbstract\nAlthoug
h 1-dimensional categories of various flavours are sufficient as\na univer
se of discourse for many applications\, the theory of categories\nthemselv
es only truly reveals itself in dimension 2. For this reason\,\nand for ot
her naturally occurring motivating examples\, it is of use to\nmake rigoro
us and study various notions of 2-dimensional category.\n\nOf particular i
nterest is the ability of notions of 2-dimensional\ncategories to introduc
e "weakness". Lifted from the confines of a\nsingle dimension we are now f
ree 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 obey functoriality to varying degrees.\n\nThe talk will take the f
orm of a high-level overview of the definitions\,\nexamples\, motivations
for\, and early theory of bi-categories\,\nmulticategories\, pseudo-double
categories and virtual double categories.\nThese definitions will be comp
ared\, 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\, when composition\nis defined by a universal property\, the complex
laws and theorems of\nnon-strict composition are automatic and functorial
ity is the natural\nresult of the graded preservation of universality.\n\n
Prerequisites:\n\n- limits in a category\, especially products and pullbac
ks\n\n- monoidal categories\, and strict/strong/lax monoidal functors\n\n-
the 2-category Cat of categories\, functors\, and natural transformations
\n\nSuggested background: \n\nWe will find motivation in theory of pro-fun
ctors\nand their composites\, as well as the theory of bi-modules over rin
gs and\ntheir tensors.\n
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:20201101T005605Z
UID:blue-jay-cat/2
DESCRIPTION:Title: Getting equipped for formal category theory\nby David J
az Myers (Johns Hopkins University) as part of Johns Hopkins Category Theo
ry Virtual Seminar\n\n\nAbstract\nIn his 1973 paper Metric Spaces\, Genera
lized Logic\, and Closed Categories\, Lawvere notes that not only are the
objects of interest in mathematics organized into categories\, they often
are categories (of some flavor) in their own right. There are many differe
nt 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 algebr
a of composition of maps\, there are many concepts in category theory whic
h are unified by their expression in the algebra of composition of natural
transformations between bimodules. This algebra of natural transformation
s 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 equi
pment.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anthony Agwu (Johns Hopkins University)
DTSTART;VALUE=DATE-TIME:20201007T210000Z
DTEND;VALUE=DATE-TIME:20201007T230000Z
DTSTAMP;VALUE=DATE-TIME:20201101T005605Z
UID:blue-jay-cat/3
DESCRIPTION:Title: Partial maps and PCAs in categories\nby Anthony Agwu (J
ohns Hopkins University) as part of Johns Hopkins Category Theory Virtual
Seminar\n\n\nAbstract\nThis talk will give a brief introduction to restric
tion categories and Turing categories\, including their motivations which
relate to partial maps and partial combinatory algebras (PCAs). First we w
ill talk about restriction categories where we'll introduce notions such a
s restriction idempotents and ways they can be split. We'll then talk abou
t how to handle products within restriction categories. After this\, we'll
introduce Turing categories and describe in depth their relationship with
partial combinatory algebras.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Campbell (Johns Hopkins University)
DTSTART;VALUE=DATE-TIME:20201028T210000Z
DTEND;VALUE=DATE-TIME:20201028T230000Z
DTSTAMP;VALUE=DATE-TIME:20201101T005605Z
UID:blue-jay-cat/4
DESCRIPTION:Title: Quillen model structures in 2-category theory\nby Alexa
nder Campbell (Johns Hopkins University) as part of Johns Hopkins Category
Theory Virtual Seminar\n\n\nAbstract\nThe goal of this talk is to introdu
ce some of the basic concepts of model category theory from the point of v
iew of a 2-category theorist. All motivation and examples will be drawn fr
om 2-category theory.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:tslil clingman (Johns Hopkins University)
DTSTART;VALUE=DATE-TIME:20201014T210000Z
DTEND;VALUE=DATE-TIME:20201014T230000Z
DTSTAMP;VALUE=DATE-TIME:20201101T005605Z
UID:blue-jay-cat/5
DESCRIPTION:Title: 2-lessons from Australian category theory: mates and do
ctrinal adjunction\nby tslil clingman (Johns Hopkins University) as part o
f Johns Hopkins Category Theory Virtual Seminar\n\n\nAbstract\nPart of the
lesson of category theory is that adjunctions permeate\nmathematics at al
most all levels\, from logic and topology to algebra and\nlanguage grammar
. The categorical method\, however\, teaches us that\nunderstanding is obt
ained by collecting our objects of interest into a\ncategory and studying
their structure -- as given by their morphisms --\nen masse. What then\, o
n this view\, is the structure supported by the\ncategory whose /objects/
are adjunctions? What is an appropriate notion\nof morphism here?\n\nIn th
is talk we will begin to answer this question in greater (but not\ngreates
t) generality by extracting\, from any 2-category\, at first a\ncategory a
nd then later double categories whose objects (and later\npro-arrows) are
adjunctions. This will allow us to see how morphisms\nbetween left adjoint
s correspond to morphisms between right adjoints\,\nthe ``mate corresponde
nce''. Then\, in the double-categorical context\, we\nwill realise mates a
s a /very/ natural isomorphism between certain\ndouble functors. We will e
xploit this naturality to give a theorem about\nthe transfer of all propos
itions and structures on left adjoints\nexpressible in a certain language\
, to corresponding propositions and\nstructures on their right adjoints. T
hat is\, we will aim to make\nrigorous Leinster's view that ``all imaginab
le statements 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 time and interest permits\, to\nthe celebrated ``Doctrinal Adjunc
tion'' result of Kelly. The central\nresult of this paper relates adjuncti
ons of lax- and colax-morphisms of\n2-dimensional algebras for 2-dimension
al monads to adjunctions of the\nunderlying objects. As a particular conse
quence\, in an adjunction of\nmonoidal categories the left adjoint is opla
x-monoidal iff. the right\nadjoint is lax-monoidal.\n\nPre-requisites:\n\n
- Adjunctions (equational definition in Cat)\n\n- 2-categories\, 2-functor
s (definitions and Cat as an example)\n\n- double categories\, double func
tors (definitions)\n\nInessential but suggested:\n\n- horizontal and verti
cal double-natural transformations\n
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:20201101T005605Z
UID:blue-jay-cat/6
DESCRIPTION:by Daniel Fuentes-Keuthan (Johns Hopkins University) as part o
f Johns Hopkins Category Theory Virtual Seminar\n\nAbstract: TBA\n
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:20201101T005605Z
UID:blue-jay-cat/7
DESCRIPTION:Title: Comparing left and right derived functors with double c
ategories\nby David Jaz Myers (Johns Hopkins University) as part of Johns
Hopkins Category Theory Virtual Seminar\n\n\nAbstract\nFor functors betwee
n abelian categories which fail to be exact\, there are left and right der
ived functors which encode obstructions to exactness on a homological leve
l. These derived functors are quite readily described using the language o
f model categories applied to categories of chain complexes. In this talk\
, we will explore the double functoriality of taking left and right derive
d functors\, and use this to give a derived version of the projection form
ula for base change along a proper map between locally compact Hausdorff s
paces.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Campbell (Johns Hopkins University)
DTSTART;VALUE=DATE-TIME:20201202T220000Z
DTEND;VALUE=DATE-TIME:20201203T000000Z
DTSTAMP;VALUE=DATE-TIME:20201101T005605Z
UID:blue-jay-cat/8
DESCRIPTION:Title: The new normal lax functors\nby Alexander Campbell (Joh
ns Hopkins University) as part of Johns Hopkins Category Theory Virtual Se
minar\n\nAbstract: TBA\n
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:20201101T005605Z
UID:blue-jay-cat/9
DESCRIPTION:Title: Universal solutions to control and design problems\nby
David Jaz Myers (Johns Hopkins University) as part of Johns Hopkins Catego
ry Theory Virtual Seminar\n\n\nAbstract\nIn systems theory\, a control pro
blem is a constraint on values of certain variables of a system's state\;
the problem is solved by the construction of a system whose state ensures
that this constraint is satisfied. Dually\, a design problem is a specific
ation of behaviors of certain variables of a system's states\; the problem
is solved by the construction of a system which implements these behavior
s. Working within the paradigms of composition framework\, I will give gen
eral formal definitions of control and design problems for all sorts of dy
namical systems. We will then see that control and design problems admit u
niversal solutions for a fairly large class of systems of various sorts (d
iscrete-time\, ODEs\, etc.) by appealing to adjoint functor theorems.\n
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