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BEGIN:VEVENT
SUMMARY:David Spivak (Topos Institute)
DTSTART;VALUE=DATE-TIME:20220125T170000Z
DTEND;VALUE=DATE-TIME:20220125T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204701Z
UID:Intercats/1
DESCRIPTION:Title: Categorical interaction in the polynomial ecosystem\nby David Spivak
(Topos Institute) as part of Intercats: Seminar on Categorical Interactio
n\n\n\nAbstract\nCategory theory offers an elegant\, compositional\, and w
ell-interoperating framework in which to formalize many different sorts of
interacting systems\, including database\, dynamical\, software\, learnin
g\, and game-playing systems. \n\nIn this talk I'll start by giving a bird
's-eye view of these applications. I'll then discuss polynomial functors a
nd the associated framed bicategory Cat# of comonoids. I'll say a bit abou
t how Cat# fits into the above stories and spend the remainder of the time
trying to give a hint as to the astounding amount of structure this categ
ory has. \n\nOne might think of Cat# like the complex numbers: simultaneou
sly extremely useful in applications and extremely mathematically well-beh
aved\, the combination of which gives a sense of its being more "part of n
ature" than "human-made".\n
LOCATION:https://researchseminars.org/talk/Intercats/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bartosz Milewski
DTSTART;VALUE=DATE-TIME:20220208T170000Z
DTEND;VALUE=DATE-TIME:20220208T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204701Z
UID:Intercats/2
DESCRIPTION:Title: Introduction to Profunctor Optics\nby Bartosz Milewski as part of In
tercats: Seminar on Categorical Interaction\n\n\nAbstract\nSet-valued func
tors are a categorical answer to linear algebra. I will introduce profunct
ors and (co-)end calculus\, and show how to use them to describe existenti
al optics and their Tambara-based representations.\n
LOCATION:https://researchseminars.org/talk/Intercats/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jules Hedges (University and College Union)
DTSTART;VALUE=DATE-TIME:20220222T170000Z
DTEND;VALUE=DATE-TIME:20220222T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204701Z
UID:Intercats/4
DESCRIPTION:Title: Lenses and their generalisations: a guide to the design space\nby Ju
les Hedges (University and College Union) as part of Intercats: Seminar on
Categorical Interaction\n\n\nAbstract\nThe number of variants of lens-lik
e structures\, plus some questionable terminology\, can seem overwhelming.
I will tour some of the main variants\, with emphasis on exactly what con
ditions on the base category are necessary for the construction\, and how
they relate to each other. We will visit: (1) lenses over a cartesian cate
gory\, (2) linear lenses over a monoidal closed category\, (3) optics over
a monoidal category\, or more generally a pair of actegories\, (4) depend
ent lenses over a category with pullbacks\, or more generally an indexed c
ategory\, and (5) polynomial natural transformations over a locally cartes
ian closed category. Unifying these motivates the problem of “dependent
optics”\, which will be the topic of several future seminars.\n\nI am on
strike action during this talk and I represent myself as an independent r
esearcher\, not my employer. I will use some of my time to discuss this. M
ore information about our grievances can be found here: https://www.ucu.or
g.uk/article/11896/Why-were-taking-action\n
LOCATION:https://researchseminars.org/talk/Intercats/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valeria de Paiva (Topos Institute)
DTSTART;VALUE=DATE-TIME:20220308T170000Z
DTEND;VALUE=DATE-TIME:20220308T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204701Z
UID:Intercats/5
DESCRIPTION:Title: Dialectica Petri Nets\nby Valeria de Paiva (Topos Institute) as part
of Intercats: Seminar on Categorical Interaction\n\n\nAbstract\nThe categ
orical modeling of Petri nets has been much investigated recently. We revi
sit the use of the Dialectica construction as a categorical model for Petr
i nets\, generalizing the original application (Brown and Gurr) to suggest
that Petri nets with different kinds of transitions can be modeled in the
same categorical framework. Transitions representing truth-values\, proba
bilities\, rates or multiplicities\, evaluated in different algebraic stru
ctures called lineales are useful and are modeled here in the same categor
y. We investigate (categorical instances of) this generalized model and it
s connections to more recent models of categorical nets.\n
LOCATION:https://researchseminars.org/talk/Intercats/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Toby St Clere Smithe (Topos Institute)
DTSTART;VALUE=DATE-TIME:20220322T170000Z
DTEND;VALUE=DATE-TIME:20220322T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204701Z
UID:Intercats/6
DESCRIPTION:Title: Categories by proxy and the limits of Para\nby Toby St Clere Smithe
(Topos Institute) as part of Intercats: Seminar on Categorical Interaction
\n\n\nAbstract\nThe notion of parameterization is of great importance in c
ategorical cybernetics\, providing space for morphisms to be learnt\, or f
or their choice to be 'externally' determined. At the same time\, the conc
ept of 'randomness pushback' tells us that the randomness of a stochastic
channel can also (in nice circumstances) be so externalized\, leaving inst
ead a random choice of deterministic map. The usual perspective on paramet
erization is an 'internal' one\, treating the parameter as a modification
of a morphism's (co)domain. In general\, however\, this perspective is not
wide enough to retain all the structure of the category at hand: an 'exte
rnal' perspective seems mathematically\, as well as philosophically\, nece
ssary. (In earlier work\, we attempted to provide such an external perspec
tive using an enriched-categorical notion of parameterization\, but this i
s similarly insufficient.)\n\nHere\, we describe an alternative perspectiv
e\, considering an internal category parameterized by its 'external' unive
rse. We build an indexed double category over the double category of spans
in the universe\, with each base object representing a choice of 'paramet
erizing context'. When the internal category has limits or a subobject cla
ssifier\, so does its parameterization\; with appropriate quotienting\, so
does the corresponding Grothendieck construction. By decorating the spans
with (sub)distributions\, the same facts hold true even in the stochastic
case\, suggesting semantics for notions of 'stochastic type' and 'stochas
tic term'. In this setting\, we can reformulate Bayesian lenses as "Bayesi
an dependent optics"\, treating generative models as such stochastic terms
.\n
LOCATION:https://researchseminars.org/talk/Intercats/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Moritz Schauer (Chalmers University and University of Gothenburg)
DTSTART;VALUE=DATE-TIME:20220503T160000Z
DTEND;VALUE=DATE-TIME:20220503T170000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204701Z
UID:Intercats/7
DESCRIPTION:Title: Bidirectional compositionality in inference and stochastic optimisation<
/a>\nby Moritz Schauer (Chalmers University and University of Gothenburg)
as part of Intercats: Seminar on Categorical Interaction\n\n\nAbstract\nBa
yesian inference\, entropy-regularised optimal transport and optimal contr
ol are linked via a variational formalism. The laws of compositionality of
the formalism are of optical nature: the Bellman principle leads to bidir
ectional (backward-forward) representation of the posterior\, the optimall
y controlled process or the optimal transport scheme. The Backward Filteri
ng Forward Guiding (BFFG) paradigm (Mider et al.\, 2020) is an extension w
hich incorporates a Monte Carlo element. This allows to formulate a set of
elementary (and\, by Monte Carlo\, tractable) transformation rules of fun
ctorial nature suitable for automatisation in probabilistic programming.\n
LOCATION:https://researchseminars.org/talk/Intercats/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruno Gavranović (University of Strathclyde)
DTSTART;VALUE=DATE-TIME:20220405T170000Z
DTEND;VALUE=DATE-TIME:20220405T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204701Z
UID:Intercats/8
DESCRIPTION:Title: Optics vs Lenses\, Operationally\nby Bruno Gavranović (University o
f Strathclyde) as part of Intercats: Seminar on Categorical Interaction\n\
n\nAbstract\nOptics\, lenses\, prisms\, and similar abstract gadgets are o
ur best friends when it comes to modelling bidirectional processes. While
optics are more general than lenses\, it's understood that they're equival
ent in the special setting of a cartesian monoidal category. Fixing the se
tting of a cartesian monoidal category\, in this talk I'll explore how thi
s equivalence is denotational in nature\, and the result of erasure of imp
ortant operational data. I'll advocate that the operational aspect is not
optional\, but rather crucial in using these gadgets to understand real-wo
rld systems.\n
LOCATION:https://researchseminars.org/talk/Intercats/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bryce Clarke (Macquarie University)
DTSTART;VALUE=DATE-TIME:20220419T160000Z
DTEND;VALUE=DATE-TIME:20220419T170000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204701Z
UID:Intercats/9
DESCRIPTION:Title: Constructing lenses in double categories\nby Bryce Clarke (Macquarie
University) as part of Intercats: Seminar on Categorical Interaction\n\n\
nAbstract\nLenses are a family of mathematical structures used to model bi
directional transformations between systems. A common feature among all ki
nds of lenses is that they consist of a "forwards" component and a "backwa
rds" component. A double category is a 2-dimensional categorical structure
consisting of objects\, two types of morphism (horizontal and vertical)\,
and cells between them. A natural question arises: what if the forwards a
nd backwards components of a lens were the horizontal and vertical morphis
ms in a double category? \n\nIn this talk\, I advocate for a double catego
rical approach to lenses\, and demonstrate how many examples of lenses\, p
articularly those satisfying "lens laws"\, may be built from the horizonta
l and vertical morphisms in a double category. A general process for const
ructing lenses inside any double category\, called the "right-connected co
mpletion"\, is introduced and is shown to satisfy a universal property. Fi
nally\, we explore how many questions and properties of lenses may be unde
rstood in the setting of double categories.\n
LOCATION:https://researchseminars.org/talk/Intercats/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eigil Fjeldgren Rischel (University of Strathclyde)
DTSTART;VALUE=DATE-TIME:20220614T160000Z
DTEND;VALUE=DATE-TIME:20220614T170000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204701Z
UID:Intercats/10
DESCRIPTION:by Eigil Fjeldgren Rischel (University of Strathclyde) as part
of Intercats: Seminar on Categorical Interaction\n\nInteractive livestrea
m: https://topos-institute.zoom.us/j/88577027154?pwd=UkNhdm1iRElnZDdhMU5rS
lRGMGlWdz09\nPassword hint: intercats\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Intercats/10/
URL:https://topos-institute.zoom.us/j/88577027154?pwd=UkNhdm1iRElnZDdhMU5r
SlRGMGlWdz09
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matteo Capucci (University of Strathclyde)
DTSTART;VALUE=DATE-TIME:20220517T160000Z
DTEND;VALUE=DATE-TIME:20220517T170000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204701Z
UID:Intercats/11
DESCRIPTION:Title: Dependent lenses are dependent optics\nby Matteo Capucci (Universit
y of Strathclyde) as part of Intercats: Seminar on Categorical Interaction
\n\n\nAbstract\nMixed optics and F-lenses are orthogonal generalizations o
f lenses\, an unreasonably effective abstraction for bidirectional process
es in cartesian categories. Mixed optics generalize lenses by dropping the
cartesianity assumption\, which makes them somehow 'linearly typed'. Inst
ead\, F-lenses generalize lenses by making them dependently typed. Both ge
neralizations greatly improve expressivity and come with compelling exampl
es.\nTherefore\, it is natural to wonder whether 'dependent mixed optics'\
, generalizing both\, are a thing. In the last six months a quick successi
on of papers (by MSP\, Milewski\, Vertechi and C.) converged to a common d
efinition. In this talk I'll review the state of the art on dependent opti
cs\, with the concrete goal of explaining Vertechi's proof that dependent
lenses (aka morphisms in Poly) are dependent optics.\n
LOCATION:https://researchseminars.org/talk/Intercats/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Keno Fischer (Julia Computing)
DTSTART;VALUE=DATE-TIME:20220628T160000Z
DTEND;VALUE=DATE-TIME:20220628T170000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204701Z
UID:Intercats/12
DESCRIPTION:by Keno Fischer (Julia Computing) as part of Intercats: Semina
r on Categorical Interaction\n\nInteractive livestream: https://topos-inst
itute.zoom.us/j/88577027154?pwd=UkNhdm1iRElnZDdhMU5rSlRGMGlWdz09\nPassword
hint: intercats\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Intercats/12/
URL:https://topos-institute.zoom.us/j/88577027154?pwd=UkNhdm1iRElnZDdhMU5r
SlRGMGlWdz09
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mario Román (Tallinn University of Technology)
DTSTART;VALUE=DATE-TIME:20220531T160000Z
DTEND;VALUE=DATE-TIME:20220531T170000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204701Z
UID:Intercats/13
DESCRIPTION:Title: Monoidal Streams\nby Mario Román (Tallinn University of Technology
) as part of Intercats: Seminar on Categorical Interaction\n\nInteractive
livestream: https://topos-institute.zoom.us/j/88577027154?pwd=UkNhdm1iREln
ZDdhMU5rSlRGMGlWdz09\nPassword hint: intercats\nView-only livestream: http
s://youtu.be/-pxFgjLJ3uM\n\nAbstract\nWe introduce monoidal streams: a gen
eralization of causal stream functions to monoidal categories. In the same
way that streams provide semantics to dataflow programming with pure func
tions\, monoidal streams provide semantics to dataflow programming with th
eories of processes represented by a symmetric monoidal category. At the s
ame time\, monoidal streams form a feedback monoidal category\, which can
be used to interpret signal flow graphs. As an example\, we study a stocha
stic dataflow language. This is joint work with Elena Di Lavore and Giovan
ni de Felice\, following the preprint "Monoidal Streams for Dataflow Progr
amming" (https://arxiv.org/abs/2202.02061).\n
LOCATION:https://researchseminars.org/talk/Intercats/13/
URL:https://topos-institute.zoom.us/j/88577027154?pwd=UkNhdm1iRElnZDdhMU5r
SlRGMGlWdz09
URL:https://youtu.be/-pxFgjLJ3uM
END:VEVENT
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