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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: T_MUUK (18.12.2000)
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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 Last update: Zakouřil Pavel, RNDr., Ph.D. (05.08.2002)
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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: T_MUUK (20.05.2004)
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