MU03260 Category Theory

Mathematical Institute in Opava
Winter 2010
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Guaranteed by
doc. RNDr. Michal Marvan, CSc.
Mathematical Institute in Opava
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Category theory provides a background for many areas of modern Mathematics. It helps to systemize the knowledge, e.g., in abstract algebra or general topology. It becomes nearly indispensable in algebraic topology. The essence of some constructions (e.g., products), which frequently appear in various areas of Mathematics, consists in ensuring commutativity of a particular diagram. In category theory they become just concrete examples of general constructions with abstract morphisms linked by abstract objects. On a higher-level of abstraction, categories are linked by functors and functors are linked by natural transformations.
Syllabus
  • Objects and morphisms, category, dual category, subcategory.
    Monomorhisms, epimorphisms, equalizers, products,
    pullbacks, general limits and dual concepts.
    Functors, concrete categories, equivalence of categories.
    Natural transformations, representable
    functors, adjoint functors, Freyd's theorems.
    Additive and Abelian categories, kernel and cokernel,
    exact functors.
    Injective and projective objects, resolvents,
    derived functors, Ext and Tor.
Literature
    recommended literature
  • S. Mac Lane. Categories for the Working Mathematician. New York, 1971. info
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
Oral examination.
The course is also listed under the following terms Winter 1999, Winter 2000, Winter 2001, Winter 2002, Winter 2003, Winter 2004, Winter 2005, Winter 2006, Winter 2007, Winter 2008, Winter 2009, Winter 2011, Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019.
  • Enrolment Statistics (Winter 2010, recent)
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