The New York City

Category Theory Seminar

Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York

Some talks will be in-person (with a Zoom connection) and some talks will only be on Zoom.
Time: Wednesdays 02:00-3:00 PM Eastern Time (US and Canada) NOTICE NEW TIME!!!

IN-PERSON INFORMATION:
365 Fifth Avenue (at 34th Street) map
(Diagonally across from the Empire State Building)
New York, NY 10016-4309
Room 4214.03 NOTICE NEW ROOM!!!
THere will be a Zoom link to join us on in-person talks. This means the talks will be hybrid.


ZOOM INFORMATION:
https://brooklyn-cuny-edu.zoom.us/j/81090491347?pwd=NnbAzAnuh70bxYsEmhJSPfxoGIP0aN.1
Meeting ID: 810 9049 1347
Passcode: 706111

Seminar web page.
Videoed talks.
Previous semesters.
List of previous speakers.
Researchseminars.org page.

Contact N. Yanofsky to schedule a speaker
or to add a name to the seminar mailing list.

Co-organizer: Emilio Minichiello.

Fall 2025



  • Speaker:     Sam McCrosson, Montana State University.

  • Date and Time:     Wednesday September 17, 2025, CANCELED.

  • Title:     Using Microsupports to Detect and Describe Constructible Sheaves.

  • Abstract: Microlocal sheaf theory has been gaining popularity recently for its applications to symplectic geometry. In this talk, we’ll explore a more topological application of this subject: how the notion of the microsupport of a sheaf can be used to tell if a sheaf is “constructible,” i.e. locally constant on strata, and if so, what the coarsest stratification is with this property.

    Versions of this result can be found as far back as Kashiwara and Schapira’s 1990 book “Sheaves on Manifolds” (which pioneered the subject of microlocal sheaf theory). Today, all sorts of generalizations are possible using schemes, \infty-categories, and other fancy machinery. This talk will focus on a particularly simple case: using 1-category theory and sheaves of sets on topological spaces to illustrate the key ideas with concrete examples.



  • Speaker:     Amartya Shekhar Dubey, National Institute of Science Education and Research.

  • Date and Time:     Wednesday October 22, 2025, 2:00 - 3:00 PM. New York time. ZOOM TALK

  • Title:     Unital k-restricted Infinity Operads.

  • Abstract: The goal is to understand unital \infty-operads by their arity restrictions. Given k \geq 1, we develop a model for unital k-restricted \infinty-operads, which are variants of \infinity-operads with (\leq k)-arity morphisms, as complete Segal presheaves on closed k-dendroidal trees built from corollas with valence \leq k. Furthermore, we prove that the restriction functors from unital \infty-operads to unital k-restricted \infty-operads admit fully faithful left and right adjoints by showing that the left and right Kan extensions preserve complete Segal objects. Varying k, the left and right adjoints give a filtration and a co-filtration for any unital \infty-operads by k-restricted \infty-operads. This is joint work with Yu Leon Liu.



  • Speaker:     Jonathon Funk, Queensborough, CUNY.

  • Date and Time:     Wednesday October 29, 2025, 7:00 - 8:30 PM. IN-PERSON TALK

  • Title:     More Toposes and C*-algebras.

    • Slides of the talk.

  • Abstract: A unital $C^*$-algebra $\mathcal{A}$ has associated with it a category $\mathcal{M}(\mathcal{A}) = \mathcal{M}$, which I call the division category of (the underlying ring of) $\mathcal{A}$. A typical object of $\mathcal{M}$ is an element of $\mathcal{A}$, denoted $R, S$ etc., and a morphism $U: R \to S$ is an element $U$ of $\mathcal{A}$ such that $\mathrm{Ann}(R) = \mathrm{Ann}(U)$ and $U = SX$ for some $X$, where $\mathrm{Ann}(R) = \{ X \in \mathcal{A} \mid RX = 0 \}$. Let $\mathscr{M}$ denote the topos of presheaves on $\mathcal{M}$. We shall discuss three aspects beginning with:

    (1) The positive quotient and polar decomposition. How does polar decomposition generalize to all unital $C^*$-algebras, and not just the supported ones? This question may be answered in terms of a canonical correspondence between wide étale subcategories of $\mathcal{M}$ and the quotients in $\mathscr{M}$ of the representable presheaf associated with the unit of $\mathcal{A}$.

    (2) The Gelfand spectrum of a commutative $C^*$-algebra: 1-dimensional representations. How this is related to $\mathcal{M}$ follows a pattern similar to the Zariski spectrum of a commutative ring.

    (3) GNS-representation theory (in any dimension), and the spectrum of an arbitrary $C^*$-algebra. One of our tools is what we shall call a seminormed $\mathcal{A}$-module, by which we mean a right $\mathcal{A}$-module $\mathcal{V}$ that carries a seminorm such that \[ \forall v \in \mathcal{V}, \; \forall U \in \mathcal{A}, \quad \|vU\| \leq \|v\| \, \|U\| . \] The functional dual $B(\mathcal{A})$, consisting of bounded $\mathbb{C}$-linear maps $\tau : \mathcal{A} \to \mathbb{C}$, is an important $\mathcal{A}$-module especially for GNS-theory. Its right action is defined by \[ \tau U(X) = \tau(XU^*), \quad \tau \in B(\mathcal{A}). \] Moreover, this action satisfies $\|\tau U\| \leq \|\tau\| \, \|U\|$, so $B(\mathcal{A})$ is a normed $\mathcal{A}$-module. $B(\mathcal{A})$ classifies functionals in the sense that for any seminormed $\mathcal{A}$-module $\mathcal{V}$ there is a natural isomorphism \[ B(\mathcal{V}) \cong \mathcal{A}\text{-Bdd}(\mathcal{V}, B(\mathcal{A})). \] Therefore, the presheaf associated with $B(\mathcal{A})$ is given by \[ \widehat{B(\mathcal{A})}(R) = \mathcal{A}\text{-Bdd}(R\mathcal{A}, B(\mathcal{A})) \;\cong\; B(R\mathcal{A}). \] From this point of view, $\widehat{B(\mathcal{A})}$ is the presheaf of functional germs on $\mathcal{A}$, suggesting that $\widehat{B(\mathcal{A})}$ may be interpreted as the complex numbers object of the topos $\mathscr{M}$. In any case, $\widehat{B(\mathcal{A})}$ is a ring object with a conjugation operation (such that $\overline{\tau}(SX) = \overline{\tau(SX)}$) internal to $\mathscr{M}$.



  • Speaker:     Florian Lengyel, CUNY.

  • Date and Time:     Wednesday November 5, 2025, 7:00 - 8:30 PM. ZOOM TALK

  • Title:     Combinatorics of Algebraic n-Hypergroupoids.

    • Paper of the talk.

  • Abstract: Let \(\vec{s}=(n_1,\dots,n_k)\in\mathbb{N}^k\) and let \(A\) be a commutative ring. We analyze the horn-filling combinatorics of the diagonal simplicial tensor module \(X_\bullet(\vec{s};A)\) to prove precise conditions on \(k\) and \(n=\min(\vec{s})-1\) that yield algebraic models of \(n\)-hypergroupoids.

    Fix \(j\in[n]\). The horn kernel \(R_{n,j}:=\bigcap_{i\ne j}\ker d_i\) measures the non-uniqueness of fillers for \((n,j)\)-horns. We prove that its basis is formed by coordinate tensors \(\{E_m\}\) where the multi-index \(m\) is missing, meaning its coordinates cover the set \([n]\setminus\{j\}\). We also prove a self-contained horn non-degeneracy lemma, \(R_{n,j}\cap D_n=\{0\}\), which confirms that these basis elements (and thus any difference between fillers) are non-degenerate. This leads to our Support Characterization Theorem: the difference between any tensor \(T\) and its canonical (Moore) filler \(T'\) lies in \(R_{n,j}\) and is supported within the set of missing indices.

    Counting missing indices via inclusion–exclusion yields exact rank formulas. This implies that fillers are non-unique (\(R_{n,j}\ne 0\)) if and only if \(k\ge n\). For the constant shape \(n_a=n+1\), we obtain \[ \mathrm{rank\,}R_{n,j}=n!\,\genfrac{\{}{\}}{0pt}{}{k}{n}+(n+1)!\,\genfrac{\{}{\}}{0pt}{}{k}{n+1}. \]
    Although \(X_\bullet(\vec{s};A)\) is acyclic, these combinatorial dichotomies prove that \(X_\bullet(\vec{s};A)\) is a strict algebraic \(n\)-hypergroupoid if and only if \(k=n\). To compute explicit generators for \(n\)-hypergroupoids, we define standard tensors to characterize when a generated sub-module \(\langle T\rangle\) faithfully reflects the combinatorics of the ambient module \(X_\bullet(\vec{s};A)\).

    A companion code repository provides the Moore filler implementation, parallel algorithms for identifying the missing index basis, and computational experiments.




  • Speaker:     Emilio Minichiello, CUNY CityTech.

  • Date and Time:     Wednesday November 12, 2025, 7:00 - 8:30 PM. IN-PERSON TALK.

  • Title:     Model Structures for Simplicial Complexes and Graphs.

  • There will be a special *pretalk* at 6:00-7:00 at the room to introduce model categories and other ideas for the talk.

  • Abstract: I’ll talk about my new paper which constructs model structures on the category of simplicial complexes and on reflexive graphs which are reminiscent of the Thomason model structure on categories. I’ll give some background and motivation for studying this and the surrounding questions of graph homotopy theory.



  • Speaker:     Evan Misshula, CUNY.

  • Date and Time:     Wednesday December 3, 2025, 7:00 - 8:30 PM. IN-PERSON TALK

  • Title:     From Outer Measures to Adjunctions: A Category-Theoretic Recasting of Caratheodory’s Extension Theorem.

  • Abstract: The Caratheodory Extension Theorem underpins modern measure theory by extending a pre-measure on an algebra to a complete measure on the generated -algebra. Traditionally, the proof proceeds through outer measures, Caratheodory measurability, and a series of delicate technical verifications – a process that reveals the "monsters" lurking in the power set but often obscures the structural simplicity of the result. In this talk, I will first outline the classical construction to highlight these subtleties, and then present a category-theoretic reformulation: the extension theorem emerges naturally from an adjunction. The categorical perspective streamlines the argument, but seeing both sides illuminates why rigor is indispensable and how category theory captures the essence of the construction.



    Spring 2026




  • Speaker:     Sergei Artemov, The CUNY Graduate Center.

  • Date and Time:     Wednesday February 4, 2026, 2:00 - 3:30 PM. IN-PERSON TALK

  • Title:     Non-compact proofs.

  • Abstract: Non-compact proofs are used in mathematics but overlooked in the analysis of (un)provability of consistency. We focus on arithmetical proofs of universal statements (*) "for any natural number n, F(n)." A proof of (*) is compact if all proofs of F(n)'s for n=0,1,2,... fit into some finitely axiomatized fragment of Peano Arithmetic PA. An example of non-compact reasoning is the standard proof of Mostowski's 1952 reflexivity theorem: PA proves the consistency of its finite fragments.

    It turns out that Gödel's Second Incompleteness Theorem prohibits compact proofs but does not rule out non-compact proofs of PA-consistency formalizable in PA. This explains why and how the recent proof of PA-consistency in PA works. It essentially formalizes in PA the explicit version of Mostowski's non-compact proof, which is not in the scope of Gödel's theorem.



  • Speaker:     David Ellerman, University of Ljubljana.

  • Date and Time:     Wednesday February 11, 2026, 2:00 - 3:30 PM. ZOOM TALK

  • Title:     A Fundamental Duality in the Exact Sciences: An Introduction to Mathematical Metaphysics.

  • Abstract: There is a fundamental duality that runs through the exact sciences. At the logical level, it is the duality between (Boolean) logic of subsets and the logic of partitions. The quantitative versions of the dual logics are logical probability theory and logical information theory. The duality accounts for the duality in the category of Sets and its opposite Sets^{op}. The partial order in the two dual logics gives the two fundamental canonical functions and the claim is that all canonical morphisms in Sets arise from those two morphisms. In physics, there is the notion of "definiteness all the way down" which arises in classical physics (Boolean logic of subsets) and dually there is the notion of definiteness only down to a certain level and then objective indefiniteness that arises in quantum physics (logic of partitions).



  • Speaker:     Ellis Cooper .

  • Date and Time:     Wednesday February 18, 2026, 2:00 - 3:30 PM. IN-PERSON TALK

  • Title:     Algebraic String Diagrams and a Manifest Covariance Theorem.

  • Abstract: Book titles such as "Covariant Physics" (Moataz H. Emam) and "Covariant Loop Quantum Gravity: An Elementary Introduction to Quantum Gravity and Spinfoam Theory" (Carlo Rovelli and Francesca Vidotto) shout the important of covariance in modern mathematical physics. In categorical terms, covariance is a family of natural isomorphisms of pairs of functors defined on the groupoid of diffeomorphisms in a category of ``domains." "Manifest covariance" is a syntactic concept arising from preservation of covariance of basic covariant tensor calculations combined by composition and product maps. Differential geometry and general relativity theory calculations are expressed by algebraic string diagrams, including the Einstein Curvature Tensor. Physical nature is categorically natural.



  • Speaker:     James Austin Myer, CUNY.

  • Date and Time:     Wednesday March 4, 2026, 2:00 - 3:30 PM. IN-PERSON TALK

  • Title:     The Bloch Material: a Simplicial Set Whose Homology is the Higher Chow Groups of Spencer Bloch.

  • Abstract: To this day, it is still unknown whether every variety enjoys a resolution of its singularities. Dennis Sullivan suggests in a 2004 memorial article for René Thom that the obstructions constructed to attack Steenrod’s problem could be adapted to handle the outstanding scenario in positive characteristic. We will discuss a construction en route to the realization of this dream: to each variety, we prescribe a simplicial set whose homology is the higher Chow groups of (Spencer) Bloch. In particular, this simplicial set recovers the topology of the analytic space associated to a variety over the complex numbers



  • Speaker:     Kristaps John Balodis, University of Calgary.

  • Date and Time:     Wednesday March 11, 2026, 2:00 - 3:30 PM. ZOOM TALK

  • Title:     A geometric introduction to the local Langlands correspondence.

  • Abstract: In this talk I will provide a non-traditional introduction to the local Langlands program for p-adic groups by framing the so-called "Galois side" geometrically. For simplicity, the primary focus will be on the "unramified" version for GL(n). The ultimate goal will be to articulate the p-adic Kazhdan-Lusztig hypothesis with accompanying examples. Along the way, I will stop to discuss some categorical aspects of the theory.



  • Speaker:     Morgan Rogers, University of Sorbonne.

  • Date and Time:     Wednesday March 25, 2026, 2:00 - 3:30 PM. ZOOM TALK

  • Title:     Ultrarings. A categorical approach to unifying boolean and algebraic descriptive complexity.

  • Abstract:

    The presentation of a commutative ring by generators and relations is (at least superficially) similar to the presentation of a first order theory in terms of sorts, function/relation symbols and axioms. More concretely, we can associate categories to rings and to theories:

    Of course, there are many other categories we could have chosen on each side, but these particular constructions admit a mutual generalization which we call ultrarings. In this talk we explain what ultrarings are, how their presentations generalize those of commutative rings and first-order theories, and how they connect to the logical approach to complexity theory (descriptive complexity). We will also sketch how we hope to exploit this connection in the future to transport tools from algebraic geometry.

    This talk is based on work with Baptiste Chanus and Damiano Mazza, https://doi.org/10.4230/LIPIcs.FSCD.2025.13, with slightly updated definitions.





  • Speaker:     Michael Lesnick, University at Albany -- SUNY.

  • Date and Time:     Wednesday April 15, 2026, 2:00 - 3:30 PM. IN-PERSON TALK

  • Title:     Limit Computation Over Posets via Minimal Initial Functors.

  • Abstract: Joint work with Tamal Dey, Department of CS, Purdue University. It is well known that limits can be computed by restricting along an initial functor, and that this often simplifies limit computation. We systematically study the algorithmic implications of this idea for diagrams indexed by a finite poset. We say an initial functor $F\colon C\to D$ with $C$ small is \emph{minimal} if the sets of objects and morphisms of $C$ each have minimum cardinality, among the sources of all initial functors with target $D$. For $Q$ a finite poset or $Q\subseteq \mathbb{N}^d$ an interval (i.e., a convex, connected subposet), we describe all minimal initial functors $F\colon P\to Q$ and in particular, show that $F$ is always a subposet inclusion. We give efficient algorithms to compute a choice of minimal initial functor. In the case that $Q\subseteq \mathbb{N}^d$ is an interval, we give asymptotically optimal bounds on $|P|$, the number of relations in $P$ (including identities), in terms of the number $n$ of minima of $Q$: We show that $|P|=\Theta(n)$ for $d\leq 3$, and $|P|=\Theta(n^2)$ for $d>3$. We apply these results to give new bounds on the cost of computing $\lim G$ for a functor $G \colon Q\to \mathbf{Vec}$ valued in vector spaces. For $Q$ connected, we also give new bounds on the cost of computing the \emph{generalized rank} of $G$ (i.e., the rank of the induced map $\lim G\to \operatorname{colim} G$), which is of interest in topological data analysis.



  • Speaker:     Gabriel Goren Roig, TBA.

  • Date and Time:     Wednesday April 22, 2026, 2:00 - 3:30 PM. ZOOM TALK

  • Title:     TBA.

  • Abstract: TBA



  • Speaker:     TBA, TBA.

  • Date and Time:     Wednesday April 29, 2026, 2:00 - 3:30 PM. IN-PERSON TALK

  • Title:     TBA.

  • Abstract: TBA



  • Speaker:     TBA, TBA.

  • Date and Time:     Wednesday May 6, 2026, 2:00 - 3:30 PM. IN-PERSON TALK

  • Title:     TBA.

  • Abstract: TBA



  • Speaker:     Emilio Minichiello, CUNY CityTech.

  • Date and Time:     Wednesday May 13, 2026, 2:00 - 3:30 PM. IN-PERSON TALK

  • Title:    Introduction to locally presentable categories.

  • Abstract: This will be an expository talk about locally presentable categories and surrounding ideas, corresponding to Appendix C of my notes https://arxiv.org/pdf/2503.20664.



  • Speaker:     TBA, TBA.

  • Date and Time:     Wednesday May 20, 2026, 2:00 - 3:30 PM. IN-PERSON TALK

  • Title:     TBA.

  • Abstract: TBA



  • Speaker:     TBA, TBA.

  • Date and Time:     Wednesday June 3, 2026, 2:00 - 3:30 PM. IN-PERSON TALK

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  • Abstract: TBA



  • Speaker:     TBA, TBA.

  • Date and Time:     Wednesday June 10, 2026, 2:00 - 3:30 PM. IN-PERSON TALK

  • Title:     TBA.

  • Abstract: TBA