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Course, academic year 2023/2024
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Homological and Homotopic Algebra - NMAG562
Title: Homologická a homotopická algebra
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: not taught
Language: English, Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: doc. RNDr. Jan Šťovíček, Ph.D.
Class: M Mgr. MSTR
M Mgr. MSTR > Volitelné
Classification: Mathematics > Algebra
Incompatibility : NALG125
Interchangeability : NALG125
Is interchangeable with: NALG125
Annotation -
Last update: T_KA (14.05.2013)
Introduction to theory of triangulated categories with focus on derived categories of rings and algebras.
Course completion requirements - Czech
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (10.06.2019)

Předmět je zakončen písemnou zkouškou.

Literature -
Last update: doc. RNDr. Jan Šťovíček, Ph.D. (13.10.2018)

G. Friedman, An elementary illustrated introduction to simplicial sets, Rocky Mountain J. Math. 42 (2012), 353-423.

P. Goerss, J. F. Jardine, Simplicial homotopy theory, Progress in Mathematics 174, Birkhäuser Verlag, 1999.

M. Hovey, Model categories, Mathematical Surveys and Monographs 63, AMS, 1999.

C. A. Weibel, An introduction to homological algebra, Cambridge University Press, 1994.

Requirements to the exam -
Last update: doc. RNDr. Jan Šťovíček, Ph.D. (13.10.2018)

The exam is oral and the requirements correspond to the topics covered by the lectures.

Syllabus -
Last update: doc. RNDr. Jan Šťovíček, Ph.D. (13.10.2018)

1. Basic facts about simplicial sets

2. Model categoires

3. Algebraic and topological examples

4. More advanced topics to choose from (homological theories, spectra, localization, K-theory)

Entry requirements -
Last update: doc. RNDr. Jan Šťovíček, Ph.D. (13.10.2018)

Basic category theory.

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