**The New York City**

**Category Theory Seminar**

**
Department of Computer Science**

Department of Mathematics

The Graduate Center of The City University of New York

365 Fifth Avenue (at 34th Street) map

(Diagonally across from the Empire State Building)

New York, NY 10016-4309

Wednesdays 7:00 - 8:30 PM.

Room 6417 .

Contact N. Yanofsky to
schedule a speaker

or to add a name to the
seminar mailing list.

**Fall 2018 **

The New York Category Theory Seminar and the New York Haskell Meetup is sponsoring a

**Topos Theory Reading Group**

We will be reading **
**## Sheaves in Geometry and Logic: A First Introduction to Topos Theory

by Saunders MacLane, Ieke Moerdijk

The list for announcements and scheduling regarding this group is also at the hott-nyc google group:

https://groups.google.com/forum/#!forum/hott-nyc

We meet the first and third Wednesdays of each month from 7:00 to 8:30 PM in Room 6417. The meetings are run by Gershom Bazerman.

Speaker: ** Christoph Dorn, Oxford University.**

Date and Time: ** Wednesday September 5, 2018, 7:00 - 8:30 PM., Room 6417.**

Title:** Associative n-categories.**

Abstract: What is a ``natural setting'' for higher category theory? In the past decades, a guiding intuition to answer this question has been provided by analogy with the homotopy hypothesis, which says that spaces are a ``natural setting'' for higher groupoids. More precisely, the analogy suggests that we can think of the building blocks of higher categories as ``directed'' n-cells and their compositions. This intuition is reflected in most approaches to higher categories. In this talk we show that n-fold categories indicate a more general point of view. N-fold categories have a geometric calculus which specializes to a geometric calculus for n-categories called calculus of ``manifold diagrams''. By a combinatorial analysis of manifolds diagrams (of which the common string diagrams are a special case) we will built a new notion of higher categories: associative n-categories. These semi-strict higher categories have powerful features: (A) They have a geometric model in manifold diagrams (B) They are equivalent to a fully weak model of higher categories, giving evidence to a (strengthened!) version of Simpson's conjecture (C) They have a formulation as categories presented by generators. In particular the latter is a powerful and novel tool, for instance, allowing us to compute with finitely generated spaces or to implement higher categories on a computer as higher inductive types.

Speaker: ** Phillip Bressie, Kansas State University.**

Date and Time: ** Wednesday October 24, 2018, 7:00 - 8:30 PM., Room 6417.**

Title:** On Tautological Globular Operads.**

Abstract: I will begin by giving a nonstandard description of the construction of the classical tautological, or endomorphism, operad taut(X) on a set X. Then I shall describe how globular operads are a strict generalization of classical operads. From this perspective a description will be given of the analogous construction for the tautological globular operad Taut(X) on a globular set X by way of describing the internal hom functor for the monoidal category Col, of collections and collection homomorphisms, with respect to the monoidal composition tensor product used to define globular operads.
Slides of the talk.

Speaker: ** André Joyal, Université du Québec à Montréal **

Date and Time: ** Friday October 26, 2018, 7:00 - 8:30 PM., Room 4102 The Science Center. (NOTICE THE SPECIAL DAY AND ROOM)**

Title:** Homotopy type theory: a new bridge between logic, category theory and topology.**

Résumé: Martin-Lôf type theory is a language for constructive mathematics
with applications to program verifications and proof assistants.
The homotopy interpretation of Martin-Lôf type theory, discovered
by Voevodsky and independantly by Awodey and Warren,
has initiated a project for a new foundation of constructive mathematics
and of homotopy theory. An elementary notion of higher topos
is emerging in the process. We shall describe the various connections
involved.
Slides of the talk.

EVENT: ** Category Theory OctoberFest 2018.**

DATE AND TIME: ** Saturday October 27, 2018, 9:00 AM - 5:00 PM.**

DATE AND TIME: ** Sunday October 28, 2018, 9:00 AM - 1:00 PM.**

PLACE:** 304 Shepard Hall; City College, CUNY; 160 Convent Ave; New York, NY 10031.**

WEB PAGE: https://ct-octoberfest.github.io/

Speaker: ** Ieke Moerdijk, University of Utrecht.**

Date and Time: ** Wednesday October 31, 2018, 7:00 - 8:30 PM., Room 6417.**

Title:** The topos of dendroidal sets.**

Abstract: The topos of simplicial sets sits as an open subtopos inside the larger topos of dendroidal sets. These two toposes are quite similar in some respects, but completely different in others. For example, dendroidal sets carry a somewhat mysterious tensor product, which coincides with the ordinary cartesian product when applied to simplicial sets. While simplicial sets generalize small categories through the construction of the nerve, dendroidal sets generalize operads in a similar way. There are various ways in which this can be expressed, some of them quite refined in terms of Quillen model categories.

Speaker: ** John Connor, The Graduate Center, CUNY.**

Date and Time: ** Wednesday November 14, 2018, 7:00 - 8:30 PM., Room 6417.**

Title:** Intuitionistic Epistemic Logic and Propositional Truncation in the Type Theory.**

Abstract: Intuitionistic Epistemic Logic (IEL) is an extension of Intuitionistic Propositional Logic introduced by Artemov and Protopopescu. IEL introduces a co-reflexive modal axiom P ⇒ (K P), where the intended interpretation of (K P) is that P is known, but a proof of P is not necessarily at hand.

In this talk I introduce an extension of the simply typed λ-calculus which is equivalent to IEL via an extension of the Curry-Howard correspondence. The categorical semantics of the type theory are interesting in that the interpretation of the modality in a syntactic category forms part of a non-idempotent monad. I will then show that by introducing a judgmental equality we transform the monad into an idempotent monad in a quotient category, and that the new monad corresponds to propositional truncation in the new calculus.

Speaker: ** Micah Miller, Borough of Manhattan Community College, CUNY.**

Date and Time: ** Wednesday November 28, 2018, 7:00 - 8:30 PM., Room 6417.**

Title:** Primer on Homotopy Limits.**

Abstract: We go over the definition of a homotopy limit of a diagram in a simplicial model category M and some elementary computations. When we have a cosimplicial object in M, we can define its totalization. The Dwyer-Kan map is a map from the totalization to the homotopy limit. Under certain conditions, this map is a natural weak equivalence. Since the totalization is easier to compute than the homotopy limit, this gives us another way to calculate homotopy limits.

Speaker: ** Alex Martsinkovsky, Northeastern University.**

Date and Time: ** Wednesday December 5, 2018, 7:00 - 8:30 PM., Room 6417.**

Title:** Stabilization of additive functors.**

Abstract: In their classical treatise on homological algebra, Cartan and Eilenberg
make a claim that ``... the right derived functors are of real interest only if [the functor
being derived] is left exact. … Similarly the left derived functors are mainly interesting
for functors which are right exact.'' The goal of this talk is to show that this may not
necessarily be true, even for the tensor product and the Hom functors. The formalism
of zeroth derived functors leads to instantaneous proofs of the theorems of Eilenberg
and Watts. Examining the canonical transformations between an additive functor and
its zeroth derived functors, one is lead to the notions of injective or projective stabilization
of the functor, originally introduced by Auslander and Bridger. This provides an extension
of the classical Auslander-Reiten formula to arbitrary modules over arbitrary rings. An
appropriately defined iteration of injective stabilization leads to an extension of Tate
homology, which is viewed as a homological counterpart of Buchweitz's construction
of Tate cohomology. Time permitting, I will mention an intriguing parallelism between
this construction and the comparison map from Steenrod-Sitnikov homology to Čech
homology.

This will be an expository talk. All terms will be defined and explained. This is joint
work with Jeremy Russell.

Previous Semesters:

Other Category Theory Seminars: