An invitation to $\infty$-categories and their use in sheaf formalisms

Speaker: Aron Heleodoro (SIMIS)

Time: 2025-11-29 13:00-18:00
Location: 1310, SIMIS
Zoom Meeting ID: 883 4839 6324 Passcode: SIMIS

摘要：

In this talk, I will give some classical examples of homotopical/homological constructions (e.g.\ derived pushforward, derived tensor product, and cotangent complex) and explain how the language of $\infty$-categories provides a more robust and powerful theory to understand these construction. Then I will give a summary of how certain useful $\infty$-categories are constructed such as: spaces, derived $R$-modules, and derived commutative algebras. In the end I will give an idea of how such formalism is applied to the construction of sheaf theories. Along the way, I will also mention many interesting results that can only be formulated using the language of $\infty$-categories.