The New York City
Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York
TIME: Wednesdays 02:00-3:00 PM New York City Time.
PLACE: 365 Fifth Avenue (at 34th Street) map
(Diagonally across from the Empire State Building)
New York, NY 10016-4309
Room 4214.03.
If you cannot join us in person, please join us on Zoom. All talks are hybrid.
ZOOM INFORMATION:
https://brooklyn-cuny-edu.zoom.us/j/86376186975?pwd=50afg19K9jUacVc7ikNa6cY0vjkwtf.1
Meeting ID: 863 7618 6975
Passcode: NYCCTS
Seminar web page.
Videoed talks.
Previous semesters.
List of previous speakers.
Researchseminars.org page.
Co-organizers: Emilio Minichiello and Noson S. Yanofsky.
Contact E. Minichiello or N. Yanofsky to
schedule a speaker
or to add a name to the
seminar mailing list.
Fall 2026
Speaker: Sridhar Ramesh
Date and Time: Wednesday September 23, 2026, 2:00 - 3:30 PM. NYC TIME.
Title: Categorical structures for Gödel incompleteness and Löb’s theorem.
Abstract: A remarkably simple category-theoretic structure serves as an abstract environment for deriving Löb’s theorem, of which Gödel's incompleteness theorems are a special case. Specifically, an “introspective theory” is any category with finite limits T, with an internal category with finite limits C, along with a natural transformation from the self-indexing of T to C (construed as contravariant functors from T to the category of categories with finite limits). Amazingly, such minimal structure is in itself enough to derive Löb’s theorem as a guarded fixed point operation!
This abstraction (originally defined in the speaker's dissertation, on which this talk is based) unifies disparate contexts of Gödel-Löb phenomena, including traditional logic or arithmetic universes a la Joyal, along with the interpretation of guarded recursion for presheaves over well-founded orders by Birkedal et al, along with the distinct classical interpretation of the GL modal logic in well-founded transitive Kripke frames. We also explore the free introspective theory, which admits an explicit description ("the theory of geminal categories"), and discuss some illuminating relationships between introspective theories and geminal categories.
Speaker: Amar Hadzihasanovic
Date and Time: Wednesday October 7, 2026, 2:00 - 3:30 PM. NYC TIME.
Title: On the coherent self-dual omega-equivalence.
Abstract: The "walking equivalence" is the 2-category free on two morphisms going in opposite directions, together with 2-morphisms witnessing that those are each other's weak inverse. This 2-category is not coherent (which, in this case, means not contractible): a coherent replacement is the "walking adjoint equivalence", where the weak invertibility witnesses additionally satisfy the triangle equations.
The same problem appears for (naive) walking equivalences between higher categories, only worse because there is no obvious fix. Recently, I, Loubaton, Ozornova, and Rovelli constructed a coherent model of the walking equivalence of omega-categories, which, however, gives up one nice property: it is not self-dual with respect to the exchange of a morphism with its weak inverse. In this talk, I will present some recent work towards the construction of a coherent self-dual model, involving an operad arising in the combinatorics of noncrossing partitions.
Speaker: Emilio Minichiello, CUNY CityTech.
Date and Time: Wednesday October 21, 2026, 2:00 - 3:30 PM. NYC TIME.
Title: Introduction to Locally Presentable Categories.
Abstract: This will be an expository talk about locally presentable categories. We will approach them in a very naive way, looking at what properties of the category of Sets we wish to generalize, and what we get from these properties. This talk will be taken from Appendix C in my notes.
Speaker: Raymond Puzio
Date and Time: Wednesday November 4, 2026, 2:00 - 3:30 PM. NYC TIME.
Title: Gaussians, Groups, and Renormalization.
Abstract: Gaussian (a.k.a. normal) probability distributions are ubiquitous. One reason for this is the fact that the set of Gaussian distributions is closed under multiple operations---subspace restriction, fiberwise integration, disjoint multiplication, pointwise multiplication, convolution. Also, as Heisenberg and Dirac realized in the early days of quantum mechanics, the Gaussian distribution may be characterized uniquely as the fixed point of a group action. In this talk, we will show how the aforementioned operations on distributions correspond to operations on groups. This provides a systematic, functorial, and generalizable approach to deriving and understanding properties of Gaussian distributions.
My interest in this topic comes from a joint project with Sam McCrosson on renormalization in quantum field theory. We used this group-theoretic approach to Gaussian distributions to derive the renormalization flow from the path integral. After a quick but self-contained introduction to renormalization, I will give an overview of this project as a practical application of the ideas presented here.
Speaker: Jonathon Funk, Queensborough, CUNY.
Date and Time: Wednesday December 2, 2026, 2:00 - 3:30 PM. NYC TIME.
Title: Sheaf theory for C(X).
Abstract: TBA
Speaker: Krista Zehr, University of Albany.
Date and Time: Wednesday December 9, 2026, 2:00 - 3:30 PM. NYC TIME.
Title: Stuff Types and Combinatorics of Locally Finite Categories.
Abstract: Joyal's combinatorial species are endofunctors on the category of finite sets and bijections which can be interpreted as a categorification of generating functions in combinatorics. Certain operations on these functors have a combinatorial interpretation, and correspond to operations on generating functions such as addition, multiplication, or differentiation. Species can be generalized to the stuff types of Baez and Dolan via groupoid cardinality, which is a generalization of the usual cardinality of finite sets to locally finite groupoids. We will discuss operations on stuff types and their combinatorial interpretations, as well as some results involving groupoid cardinality. If time permits, we will discuss q-analogues of stuff types, with connections to modular representation theory.
Speaker: Noson S. Yanofsky, Brooklyn College.
Date and Time: Wednesday December 16, 2026, 2:00 - 3:30 PM. NYC TIME.
Title: Syntax, Semantics, and the Philosophy of Science.
Abstract: Science describes the universe. The phenomena of the universe form one collection and the scientific descriptions form
another. These two collections are related in various ways. F.W. Lawvere's functorial semantics showed us how to deal with algebraic structure and descriptions
of algebraic structure. The semantics-syntax adjunction relates these two collections. We shall show that using the ideas of functorial semantics gives us ways of
describing many issues in the philosophy of science. We also show that many limitations of science (including epistemic boundaries and self-referential paradoxes) can be understood and classified from this point of view.
Spring 2027
Speaker: TBA, TBA.
Date and Time: Wednesday February 3, 2027, 2:00 - 3:30 PM. NYC TIME.
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Date and Time: Wednesday February 10, 2027, 2:00 - 3:30 PM. NYC TIME.
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Date and Time: Wednesday February 24, 2027, 2:00 - 3:30 PM. NYC TIME.
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Date and Time: Wednesday March 3, 2027, 2:00 - 3:30 PM. NYC TIME.
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Date and Time: Wednesday March 17, 2027, 2:00 - 3:30 PM. NYC TIME.
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Date and Time: Wednesday April 7, 2027, 2:00 - 3:30 PM. NYC TIME.
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Date and Time: Wednesday April 14, 2027, 2:00 - 3:30 PM. NYC TIME.
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Date and Time: Wednesday May 5, 2027, 2:00 - 3:30 PM. NYC TIME.
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Date and Time: Wednesday May 12, 2027, 2:00 - 3:30 PM. NYC TIME.
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Date and Time: Wednesday May 19, 2027, 2:00 - 3:30 PM. NYC TIME.
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