Infinity categories

Đang cập nhật

Tài liệu tham khảo chính được sử dụng trong seminar này là cuốn sách Higher categories and homotopical algebra (Cambridge University Press 2019) của Denis-Charles Cisinski.

This book provides an introduction to modern homotopy theory through the lens of higher categories after Joyal and Lurie, giving access to methods used at the forefront of research in algebraic topology and algebraic geometry in the twenty-first century. The text starts from scratch – revisiting results from classical homotopy theory such as Serre’s long exact sequence, Quillen’s theorems A and B, Grothendieck’s smooth/proper base change formulas and the construction of the Kan–Quillen model structure on simplicial sets – and develops an alternative to a significant part of Lurie’s definitive reference Higher topos theory, with new constructions and proofs, in particular, the Yoneda lemma and Kan extensions. The strong emphasis on homotopical algebra provides clear insights into classical constructions such as calculus of fractions, homotopy limits and derived functors, which are revisited in this enhanced context. For graduate students and researchers from neighbouring fields, this book is a userfriendly guide to the advanced tools that the theory provides for applications in such areas as algebraic geometry, representation theory, algebra and logic.

Một số tài liệu tham khảo khác về Infinity category:

• Jacob Lurie, Kerodon

• Jacob Lurie, Higher topos theory

• Jacob Lurie, Higher algebra

• Emily Riehl and Dominic Verity, Elements of Infinity Category Theory

• Moritz Groth, A short course on Infinity categories

• (Đang cập nhật)