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BEGIN:VEVENT
SUMMARY:David Spivak (Topos Institute)
DTSTART:20220125T170000Z
DTEND:20220125T180000Z
DTSTAMP:20260422T225800Z
UID:Intercats/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Intercats/1/
 ">Categorical interaction in the polynomial ecosystem</a>\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:20220208T170000Z
DTEND:20220208T180000Z
DTSTAMP:20260422T225800Z
UID:Intercats/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Intercats/2/
 ">Introduction to Profunctor Optics</a>\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:20220222T170000Z
DTEND:20220222T180000Z
DTSTAMP:20260422T225800Z
UID:Intercats/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Intercats/4/
 ">Lenses and their generalisations: a guide to the design space</a>\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:20220308T170000Z
DTEND:20220308T180000Z
DTSTAMP:20260422T225800Z
UID:Intercats/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Intercats/5/
 ">Dialectica Petri Nets</a>\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:20220322T170000Z
DTEND:20220322T180000Z
DTSTAMP:20260422T225800Z
UID:Intercats/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Intercats/6/
 ">Categories by proxy and the limits of Para</a>\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:20220503T160000Z
DTEND:20220503T170000Z
DTSTAMP:20260422T225800Z
UID:Intercats/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Intercats/7/
 ">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:20220405T170000Z
DTEND:20220405T180000Z
DTSTAMP:20260422T225800Z
UID:Intercats/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Intercats/8/
 ">Optics vs Lenses\, Operationally</a>\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:20220419T160000Z
DTEND:20220419T170000Z
DTSTAMP:20260422T225800Z
UID:Intercats/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Intercats/9/
 ">Constructing lenses in double categories</a>\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:Matteo Capucci (University of Strathclyde)
DTSTART:20220517T160000Z
DTEND:20220517T170000Z
DTSTAMP:20260422T225800Z
UID:Intercats/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Intercats/11
 /">Dependent lenses are dependent optics</a>\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:20220628T160000Z
DTEND:20220628T170000Z
DTSTAMP:20260422T225800Z
UID:Intercats/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Intercats/12
 /">Optics in the wild: reverse mode automatic differentiation in Julia</a>
 \nby Keno Fischer (Julia Computing) as part of Intercats: Seminar on Categ
 orical Interaction\n\n\nAbstract\nUsing categorical inspiration in real wo
 rld software systems: "I'll definitely be talking about the optics formali
 sm of reverse mode automatic differentiation\, but if I have space\, I mig
 ht end up talking about some more recent work also."\n
LOCATION:https://researchseminars.org/talk/Intercats/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mario Román (Tallinn University of Technology)
DTSTART:20220531T160000Z
DTEND:20220531T170000Z
DTSTAMP:20260422T225800Z
UID:Intercats/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Intercats/13
 /">Monoidal Streams</a>\nby Mario Román (Tallinn University of Technology
 ) as part of Intercats: Seminar on Categorical Interaction\n\n\nAbstract\n
 We introduce monoidal streams: a generalization of causal stream functions
  to monoidal categories. In the same way that streams provide semantics to
  dataflow programming with pure functions\, monoidal streams provide seman
 tics to dataflow programming with theories of processes represented by a s
 ymmetric monoidal category. At the same time\, monoidal streams form a fee
 dback monoidal category\, which can be used to interpret signal flow graph
 s. As an example\, we study a stochastic dataflow language. This is joint 
 work with Elena Di Lavore and Giovanni de Felice\, following the preprint 
 "Monoidal Streams for Dataflow Programming" (https://arxiv.org/abs/2202.02
 061).\n
LOCATION:https://researchseminars.org/talk/Intercats/13/
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