The basic notions and facts of category theory are presented, namely
category and subcategory, covariant and contravariant functors, full
and faithful, hom-functors, natural transfomations and the functor
categories, Yoneda lemma; limits and colimits of diagrams, Maranda's
and Mitchel's theorems; adjoint functors, free functors, reflective
and coreflective subcategories, closed and Cartesian closed categories,
contravariant adjoints and dualities; comma-categories; Adjoint Functor
Theorem and Special Adjoint Functor Theorem; extremal and regular
monomorphisms (epimorphisms), factorization systems.
For all the above, many examples and some applications are given.
Last update: ()
Úvodní přednáška z teorie kategorií, na kterou navazují další přednášky.
Literature - Czech
Last update: RNDr. Pavel Zakouřil, Ph.D. (05.08.2002)
1) S. MacLane: Categories for the Working Mathematician , Springer Verlag, Berlin, 1971
2) J. Adámek, H. Herrlich, G. Strecker: Abstract and Concrete Categories , John Wiley, New York, 1990
Syllabus -
Last update: T_MUUK (20.05.2004)
The basic notions and facts of category theory are presented, namely
category and subcategory, covariant and contravariant functors, full
and faithful, hom-functors, natural transfomations and the functor
categories, Yoneda lemma; limits and colimits of diagrams, Maranda's
and Mitchel's theorems; adjoint functors, free functors, reflective
and coreflective subcategories, closed and Cartesian closed categories,
contravariant adjoints and dualities; comma-categories; Adjoint Functor
Theorem and Special Adjoint Functor Theorem; extremal and regular