2022/2023

Introduction to Category Theory and Homological Algebra

Type: Optional course (faculty)

Delivered by: Faculty of Mathematics

When: 3, 4 module

Open to: students of all HSE University campuses

Instructors: Alexander Pavlov

Language: English

ECTS credits: 6

Contact hours: 72

Course Syllabus

Abstract

This is an introductory course in category theory and homological algebra. In the first part we cover basics of the category theory with main focus on universal construction (limits and colimits). The category theory is a universal mathematical language that has applications in many areas on mathematics, it allows us to illustrate all definition and theorems with examples from algebra, topology and geometry. After this focus on the categories that resemble categories of modules (abelian categories) and develop resolutions of objects in such categories. Using resolutions we define derived functors. The second half of the course is about general properties and examples of derived functors.