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 2015 to 2017 |
| 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: |
Czech |
| Teaching methods: |
full-time |
| Teaching methods: |
full-time |
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| Annotation -
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Last update: T_KA (14.05.2013)
Introduction to theory of triangulated categories with focus on derived categories of rings and algebras.
Last update: T_KA (14.05.2013)
Úvod do teorie triangulovaných kategorií s důrazem na derivované kategorie okruhů a algeber.
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| Literature -
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Last update: doc. RNDr. Jan Šťovíček, Ph.D. (13.10.2018)
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: doc. RNDr. Jan Šťovíček, Ph.D. (13.10.2018)
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.
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| Syllabus -
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Last update: doc. RNDr. Jan Šťovíček, Ph.D. (13.10.2018)
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: doc. RNDr. Jan Šťovíček, Ph.D. (13.10.2018)
1. Abelovské kategorie, Yonedova definice funktoru Ext.
2. Frobeniovy exaktní kategorie a jejich stabilní kategorie modulo projektivní objekty.
3. Triangulované kategorie a jejich vlastnosti.
4. Verdierova lokalizace, derivované kategorie a jejich vlastnosti.
5. Derivované ekvivalence a derivované funktory.
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| Entry requirements -
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Last update: doc. RNDr. Jan Šťovíček, Ph.D. (13.10.2018)
Basics of theory of modules (to the extent of lecture NALG028) and basic homological algebra (the Ext and Tor functors).
Last update: doc. RNDr. Jan Šťovíček, Ph.D. (13.10.2018)
Základy teorie modulů (v rozsahu přednášky NALG028) a základy homologické algebry (funktory Ext a Tor).
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