Скачать или смотреть Brandon Shapiro: Familial and Polynomial Functors for Higher Category Theories

Title: Familial and Polynomial Functors for Higher Category Theories
Speaker: Brandon Shapiro (Cornell)

Abstract: Familial functors between presheaf categories (sometimes called parametric right adjoints) arise in both the theories of databases and algebraic higher categories. Algebras for any familial monad can be treated as a type of higher category, where the cell shapes may differ from vertices and arrows, and many classical features of category theory generalize to this "shape independent" setting. Familial monads are equivalent to certain "schema" for types of higher categories, given in terms of the underlying cell shapes and their composition operations. I will describe how the proof of this equivalence uses the relationship between familial and polynomial functors, and discuss connections between higher categories and databases.

Topos Institute Berkeley Seminar
December 13, 2021