#### Fall 2021 program

###### The live HoTT Seminar is back!

Fridays 1-3pm in BH 235A

September 10, **Reid Barton** — *TBA*

September 17, **Mathieu Anel** — *Localizations of categories (part 1)*

I will review a number of results around localizations of categories, both in the context of 1‑categories and ∞‑categories. The purpose is to present homotopy theory as a toolbox to compute within ∞‑localizations, as developped in Cisinski's book. (The talk will go over some of the material presented here.)

September 24, **Jacob Neumann** — *Groundwork to Higher Allegory Theory*

I will enumerate several interesting possible avenues of research which connect the theory of binary relations to Homotopy Type Theory. Binary relations are indispensable in classical mathematics, and higher-dimensional analogues of binary relations promise to occupy an important (and interesting!) place in univalent mathematics. After rehearsing some of the theory of allegories in the setting of homotopy type theory (and speculating about possible generalizations), I'll discuss how we can adapt certain allegory-theoretic notions to better describe and reason about constructions in type theory. If possible, I hope to also touch on some semantic considerations related to this work, as well as describe some circumstances in functional programming and type theory where binary relations are particularly helpful. The content of this talk is all very much work-in-progress, so suggestions & feedback are very welcome!

October 1, **Mathieu Anel** — *Localizations of categories (part 2)*

October 8, **Mathieu Anel** — *Localizations of categories (part 3)*

October 15, **No seminar** (MURI Meeting)

October 22, **TBA** — *The small object argument*

October 29, **Jonas Frey** — *The fat small object argument*

November 5, **TBA** — *Variation on the small object argument*

Earlier seminars are listed here.