2022/2023
Научно-исследовательский семинар "Гомотопическая алгебра и теория топосов"
Статус:
Дисциплина общефакультетского пула
Когда читается:
3, 4 модуль
Охват аудитории:
для своего кампуса
Язык:
английский
Кредиты:
6
Контактные часы:
72
Course Syllabus
Abstract
One of the main reasons for significant interest in abstract homotopy theory nowadays areits applications to geometry. One of the key objects in this regard are topoi and higher topoi. At this coursewe will study homotopical instruments required for working with higher sheaves and apply this knowledge tothe study of topoi. Time permitting we will also cover applications of this theory to classical geometry such astheory of foliations.The course similarly to the course «Introduction to homotopical algebra and simplicial topology» will happenon two different weekdays. On one of them we will cover advanced homotopy theory, while on the other wewill work with geometric part of the theory.PREREQUISITES:Courses «Introduction to Homological Algebra and Category Theory» (taught by A. Goro-dentsev or C. Brav), «Algebraic topology» (taught by M. Finkelberg or M. Kasaryan), «Introduction to Homo-topical Algebra and Simplicial Topology». The last course is not necessary if one is familiar with basics ofsimplicial homotopy theory and theory of model categories.