Logic and Category Theory Seminar

The Logic and Category Theory Seminar brings together researchers working in category theory, higher category theory, logic, homotopy theory, type theory, and neighboring areas. The seminar is based at the University of Ottawa and welcomes participants from the broader mathematical community, with many talks also accessible online.

Members of the Logic and Category Theory group at the University of Ottawa include Richard Blute, Simon Henry, Rory Lucyshyn-Wright, Martina Rovelli, Ali Hamad, Daniel Almeida, Jean-Baptiste Vienney, Stefano Luneia, Arghan Dutta, Thu Ho and Amélie Comtois.

We also advertise selected talks from related seminars and events, such as the ItaCa Fest, the uOttawa Math + Stat Colloquium and the Category Theory Octoberfest, that we think may be of interest to our community.

Everyone is welcome. If you would like to give a talk, suggest a speaker, or receive seminar announcements, please contact Martina Rovelli or Stefano Luneia.

Past talks

September 17, 2026 (4:00 PM EDT)

In person in STEM 664 and online via Zoom

Richard Blute (University of Ottawa)

Quantum Finiteness Spaces

A result of Coecke, Pavlovic and Vicary states that a basis for a finite-dimensional Hilbert space can be equivalently characterised as a commutative dagger-Frobenius monoid in the category of finite-dimensional Hilbert spaces. This can be extended to an equivalence between such Frobenius algebras and the category of finite sets.

We describe an ongoing project to attempt to extend this result beyond finite sets. This requires on the one hand replacing the category of sets with the category of Ehrhard’s finiteness spaces, one of the motivating examples for the theory of differential linear logic. On the other hand, Frobenius algebras must be replaced by linear monoids as defined by Priyaa Srivinvasan.

Slides

Next talk

October 8, 2026 (4:00 PM EDT)

Online via Zoom

Rory Lucyshyn-Wright (Brandon University)

Cartesian Theories and Their Infinitary Generalization

Regular logic is the fragment of first-order logic in which only finite conjunction and existential quantification are permitted, and it admits a semantics in regular categories. Cartesian logic is a still more restrictive system of first-order logic that admits a semantics in arbitrary categories with finite limits, by allowing only finite conjunction and provably unique existential quantification. Cartesian theories were introduced by Coste, who showed that their categories of models are equivalently locally finitely presentable categories. In this talk on recent joint work with Andrew Krenz, we discuss an infinitary generalization of cartesian logic that admits a semantics in categories with 𝛼-small limits, for a regular cardinal 𝛼. We establish a complete deductive system of 𝛼-ary cartesian logic, and we define a notion of 𝛼-ary cartesian theory whose categories of models are equivalently locally 𝛼-presentable categories.

Slides Zoom Link

Upcoming talks

October 15, 2026

4:00 PM EDT· In person and online via Zoom

Simon Henry (University of Ottawa)

Rewriting for ∞-categories

Rewriting theory is a set of methods that, among other things, given a "nice enough" presentation of an algebraic structure, for example a monoid, allows to compute some closely related homotopy-theoretic structure, for example its homology or a cellular decomposition of its classifying space. I will give a brief introduction to rewriting and show how it can be used to, starting from a "nice presentation" of a category ( a convergent rewriting system) give an explicit homotopy coherent presentation of it as an infinity-category. The result is, as far as I know, new in this form, but its proof can actually be found in an old paper of Brown that predates the theory of quasicategories. This has lots of nice and simple applications to the theory of quasicategories, and I will present some of them.

Slides Zoom Link

October 20, 2026

ItaCa Fest

9:00 AM EDT· Online via Zoom