BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:David Spivak (Topos Institute) DTSTART:20220125T170000Z DTEND:20220125T180000Z DTSTAMP:20260404T111000Z UID:Intercats/1 DESCRIPTION:Title: Categorical interaction in the polynomial ecosystem\nby David Spivak (Topos Institute) as part of Intercats: Seminar on Categorical Int eraction\n\n\nAbstract\nCategory theory offers an elegant\, compositional\ , and well-interoperating framework in which to formalize many different s orts of interacting systems\, including database\, dynamical\, software\, learning\, 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 fun ctors and the associated framed bicategory Cat# of comonoids. I'll say a b it about how Cat# fits into the above stories and spend the remainder of t he time trying to give a hint as to the astounding amount of structure thi s category has. \n\nOne might think of Cat# like the complex numbers: simu ltaneously extremely useful in applications and extremely mathematically w ell-behaved\, the combination of which gives a sense of its being more "pa rt of nature" than "human-made".\n LOCATION:https://stable.researchseminars.org/talk/Intercats/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Bartosz Milewski DTSTART:20220208T170000Z DTEND:20220208T180000Z DTSTAMP:20260404T111000Z UID:Intercats/2 DESCRIPTION:Title: Introduction to Profunctor Optics\nby Bartosz Milewski as par t of Intercats: Seminar on Categorical Interaction\n\n\nAbstract\nSet-valu ed functors are a categorical answer to linear algebra. I will introduce p rofunctors and (co-)end calculus\, and show how to use them to describe ex istential optics and their Tambara-based representations.\n LOCATION:https://stable.researchseminars.org/talk/Intercats/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Jules Hedges (University and College Union) DTSTART:20220222T170000Z DTEND:20220222T180000Z DTSTAMP:20260404T111000Z UID:Intercats/4 DESCRIPTION:Title: Lenses and their generalisations: a guide to the design space \nby Jules Hedges (University and College Union) as part of Intercats: Sem inar on Categorical Interaction\n\n\nAbstract\nThe number of variants of l ens-like structures\, plus some questionable terminology\, can seem overwh elming. I will tour some of the main variants\, with emphasis on exactly w hat conditions on the base category are necessary for the construction\, a nd how they relate to each other. We will visit: (1) lenses over a cartesi an category\, (2) linear lenses over a monoidal closed category\, (3) opti cs over a monoidal category\, or more generally a pair of actegories\, (4) dependent lenses over a category with pullbacks\, or more generally an in dexed category\, and (5) polynomial natural transformations over a locally cartesian closed category. Unifying these motivates the problem of “dep endent optics”\, which will be the topic of several future seminars.\n\n I am on strike action during this talk and I represent myself as an indepe ndent researcher\, not my employer. I will use some of my time to discuss this. More information about our grievances can be found here: https://www .ucu.org.uk/article/11896/Why-were-taking-action\n LOCATION:https://stable.researchseminars.org/talk/Intercats/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Valeria de Paiva (Topos Institute) DTSTART:20220308T170000Z DTEND:20220308T180000Z DTSTAMP:20260404T111000Z 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\nTh e categorical modeling of Petri nets has been much investigated recently. We revisit the use of the Dialectica construction as a categorical model f or Petri 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\ , probabilities\, rates or multiplicities\, evaluated in different algebra ic structures called lineales are useful and are modeled here in the same category. We investigate (categorical instances of) this generalized model and its connections to more recent models of categorical nets.\n LOCATION:https://stable.researchseminars.org/talk/Intercats/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Toby St Clere Smithe (Topos Institute) DTSTART:20220322T170000Z DTEND:20220322T180000Z DTSTAMP:20260404T111000Z 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 Inte raction\n\n\nAbstract\nThe notion of parameterization is of great importan ce in categorical cybernetics\, providing space for morphisms to be learnt \, or for their choice to be 'externally' determined. At the same time\, t he concept of 'randomness pushback' tells us that the randomness of a stoc hastic channel can also (in nice circumstances) be so externalized\, leavi ng instead a random choice of deterministic map. The usual perspective on parameterization is an 'internal' one\, treating the parameter as a modifi cation 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: a n 'external' perspective seems mathematically\, as well as philosophically \, necessary. (In earlier work\, we attempted to provide such an external perspective using an enriched-categorical notion of parameterization\, but this is similarly insufficient.)\n\nHere\, we describe an alternative per spective\, considering an internal category parameterized by its 'external ' universe. We build an indexed double category over the double category o f spans in the universe\, with each base object representing a choice of ' parameterizing context'. When the internal category has limits or a subobj ect classifier\, so does its parameterization\; with appropriate quotienti ng\, so does the corresponding Grothendieck construction. By decorating th e spans with (sub)distributions\, the same facts hold true even in the sto chastic case\, suggesting semantics for notions of 'stochastic type' and ' stochastic term'. In this setting\, we can reformulate Bayesian lenses as "Bayesian dependent optics"\, treating generative models as such stochasti c terms.\n LOCATION:https://stable.researchseminars.org/talk/Intercats/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Moritz Schauer (Chalmers University and University of Gothenburg) DTSTART:20220503T160000Z DTEND:20220503T170000Z DTSTAMP:20260404T111000Z UID:Intercats/7 DESCRIPTION:Title: Bidirectional compositionality in inference and stochastic optimi sation\nby Moritz Schauer (Chalmers University and University of Gothe nburg) as part of Intercats: Seminar on Categorical Interaction\n\n\nAbstr act\nBayesian inference\, entropy-regularised optimal transport and optima l control are linked via a variational formalism. The laws of compositiona lity of the formalism are of optical nature: the Bellman principle leads t o bidirectional (backward-forward) representation of the posterior\, the o ptimally controlled process or the optimal transport scheme. The Backward Filtering Forward Guiding (BFFG) paradigm (Mider et al.\, 2020) is an exte nsion which incorporates a Monte Carlo element. This allows to formulate a set of elementary (and\, by Monte Carlo\, tractable) transformation rules of functorial nature suitable for automatisation in probabilistic program ming.\n LOCATION:https://stable.researchseminars.org/talk/Intercats/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Bruno Gavranović (University of Strathclyde) DTSTART:20220405T170000Z DTEND:20220405T180000Z DTSTAMP:20260404T111000Z UID:Intercats/8 DESCRIPTION:Title: Optics vs Lenses\, Operationally\nby Bruno Gavranović (Unive rsity of Strathclyde) as part of Intercats: Seminar on Categorical Interac tion\n\n\nAbstract\nOptics\, lenses\, prisms\, and similar abstract gadget s are our best friends when it comes to modelling bidirectional processes. While optics are more general than lenses\, it's understood that they're equivalent in the special setting of a cartesian monoidal category. Fixing the setting of a cartesian monoidal category\, in this talk I'll explore how this equivalence is denotational in nature\, and the result of erasure of important operational data. I'll advocate that the operational aspect is not optional\, but rather crucial in using these gadgets to understand real-world systems.\n LOCATION:https://stable.researchseminars.org/talk/Intercats/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Bryce Clarke (Macquarie University) DTSTART:20220419T160000Z DTEND:20220419T170000Z DTSTAMP:20260404T111000Z UID:Intercats/9 DESCRIPTION:Title: Constructing lenses in double categories\nby Bryce Clarke (Ma cquarie University) as part of Intercats: Seminar on Categorical Interacti on\n\n\nAbstract\nLenses are a family of mathematical structures used to m odel bidirectional transformations between systems. A common feature among all kinds of lenses is that they consist of a "forwards" component and a "backwards" component. A double category is a 2-dimensional categorical st ructure consisting of objects\, two types of morphism (horizontal and vert ical)\, and cells between them. A natural question arises: what if the for wards and backwards components of a lens were the horizontal and vertical morphisms in a double category? \n\nIn this talk\, I advocate for a double categorical approach to lenses\, and demonstrate how many examples of len ses\, particularly those satisfying "lens laws"\, may be built from the ho rizontal and vertical morphisms in a double category. A general process fo r constructing lenses inside any double category\, called the "right-conne cted completion"\, is introduced and is shown to satisfy a universal prope rty. Finally\, we explore how many questions and properties of lenses may be understood in the setting of double categories.\n LOCATION:https://stable.researchseminars.org/talk/Intercats/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Matteo Capucci (University of Strathclyde) DTSTART:20220517T160000Z DTEND:20220517T170000Z DTSTAMP:20260404T111000Z UID:Intercats/11 DESCRIPTION:Title: Dependent lenses are dependent optics\nby Matteo Capucci (Un iversity of Strathclyde) as part of Intercats: Seminar on Categorical Inte raction\n\n\nAbstract\nMixed optics and F-lenses are orthogonal generaliza tions of lenses\, an unreasonably effective abstraction for bidirectional processes in cartesian categories. Mixed optics generalize lenses by dropp ing the cartesianity assumption\, which makes them somehow 'linearly typed '. Instead\, F-lenses generalize lenses by making them dependently typed. Both generalizations greatly improve expressivity and come with compelling examples.\nTherefore\, it is natural to wonder whether 'dependent mixed o ptics'\, generalizing both\, are a thing. In the last six months a quick s uccession of papers (by MSP\, Milewski\, Vertechi and C.) converged to a c ommon definition. In this talk I'll review the state of the art on depende nt optics\, with the concrete goal of explaining Vertechi's proof that dep endent lenses (aka morphisms in Poly) are dependent optics.\n LOCATION:https://stable.researchseminars.org/talk/Intercats/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Keno Fischer (Julia Computing) DTSTART:20220628T160000Z DTEND:20220628T170000Z DTSTAMP:20260404T111000Z UID:Intercats/12 DESCRIPTION:Title: Optics in the wild: reverse mode automatic differentiation in Ju lia\nby Keno Fischer (Julia Computing) as part of Intercats: Seminar o n Categorical Interaction\n\n\nAbstract\nUsing categorical inspiration in real world software systems: "I'll definitely be talking about the optics formalism of reverse mode automatic differentiation\, but if I have space\ , I might end up talking about some more recent work also."\n LOCATION:https://stable.researchseminars.org/talk/Intercats/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Mario Román (Tallinn University of Technology) DTSTART:20220531T160000Z DTEND:20220531T170000Z DTSTAMP:20260404T111000Z UID:Intercats/13 DESCRIPTION:Title: Monoidal Streams\nby Mario Román (Tallinn University of Tec hnology) as part of Intercats: Seminar on Categorical Interaction\n\n\nAbs tract\nWe introduce monoidal streams: a generalization of causal stream fu nctions to monoidal categories. In the same way that streams provide seman tics to dataflow programming with pure functions\, monoidal streams provid e semantics to dataflow programming with theories of processes represented by a symmetric monoidal category. At the same time\, monoidal streams for m a feedback monoidal category\, which can be used to interpret signal flo w graphs. As an example\, we study a stochastic dataflow language. This is joint work with Elena Di Lavore and Giovanni de Felice\, following the pr eprint "Monoidal Streams for Dataflow Programming" (https://arxiv.org/abs/ 2202.02061).\n LOCATION:https://stable.researchseminars.org/talk/Intercats/13/ END:VEVENT END:VCALENDAR