Úvodní přednáška z teorie kategorií, na kterou navazují další přednášky.

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.

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

Základní kurs z teorie kategorií pro směr Matematické struktury. Přednáška seznamuje se základními pojmy a větami.

1) Pojem kategorie, funktoru, přirozené transformace, kategorie malé a konkretizovatelné.

2) Diagramy, jejich limity a kolimity, Marandova věta, zachovávání limit a kolimit.

3) Kategorie funktorů, Yonedovo lemma a Yonedovo vnoření, použití.

4) Adjunkty, věty o adjunktech, použití.

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.