2024/2025
Introduction to Category Theory and Homological Algebra
Type:
Optional course (faculty)
Delivered by:
Faculty of Mathematics
Where:
Faculty of Mathematics
When:
3, 4 module
Open to:
students of one campus
Instructors:
Alexander Pavlov
Language:
English
ECTS credits:
6
Course Syllabus
Abstract
The theory of categories provides tools for studying the relations between different areas of mathematics, especially between topology, geometry, and algebra. Homological algebra in particular grew out algebraic topology and is now widely used in representation theory and algebraic geometry.
Learning Objectives
- The lectures will introduce basic theory and examples, while examples and applications will be explored more deeply in the seminar.
Expected Learning Outcomes
- Fluency in functorial arguments in homological algebra and topology. Familiarity with fundamental examples and calculations.
Course Contents
- Basics of category theory
- Examples and applications
- Basics of homological algebra
- Differential graded algebra
- Categorical examples
Interim Assessment
- 2024/2025 4th module0.1S+0.2Q+0.3M+0.4F, where S is grade for participation in tutorials, Q is quiz grade for 4 one-hour long quizzes, M is the midterm grade, F is final exam grade.
