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Regular version of the site
2024/2025

Introduction to Category Theory and Homological Algebra

Type: Optional course (faculty)
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

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

Expected Learning Outcomes

  • Fluency in functorial arguments in homological algebra and topology. Familiarity with fundamental examples and calculations.
Course Contents

Course Contents

  • Basics of category theory
  • Examples and applications
  • Basics of homological algebra
  • Differential graded algebra
  • Categorical examples
Assessment Elements

Assessment Elements

  • non-blocking Activity
  • non-blocking Quiz
  • non-blocking Midterm grade
  • non-blocking Exam
Interim Assessment

Interim Assessment

  • 2024/2025 4th module
    0.1S+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.
Bibliography

Bibliography

Recommended Core Bibliography

  • Курс алгебры, Винберг, Э. Б., 2013

Recommended Additional Bibliography

  • Weibel, C. A. (1994). An Introduction to Homological Algebra. Cambridge University Press.

Authors

  • PAVLOV ALEKSANDR BORISOVICH
  • Иконописцева Юлия Вахтаногвна
  • BRAV Kristofer Ira