Subjects

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Homological and Homotopic Algebra - NALG125

Title:	Homologická a homotopická algebra
Guaranteed by:	Department of Algebra (32-KA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2018
Semester:	summer
E-Credits:	3
Hours per week, examination:	summer s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	cancelled
Language:	Czech
Teaching methods:	full-time

Annotation -

Introduction to theory of triangulated categories with focus on derived categories of rings and algebras.

Last update: T_KA (19.05.2009)

Literature -

A. Neeman, Triangulated categories, Princeton University Press, 2001.

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

D. Happel, Triangulated categories in the representation theory of finite-dimensional algebras, Cambridge University Press, 1988.

Last update: T_KA (19.05.2009)

Syllabus -

1. Abelian categories, Yoneda's definition of Ext.

2. Frobenius exact categories and their stable categories modulo projective objects.

3. Triangulated categories and their properties.

4. Verdier localization, derived categories and their properties.

5. Derived equivalences and derived functors.

Last update: T_KA (19.05.2009)

Entry requirements -

Basics of theory of modules (to the extent of lecture NALG028) and basic homological algebra (the Ext and Tor functors).

Last update: T_KA (19.05.2009)