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Last update: T_KAM (24.03.2004)
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Last update: prof. RNDr. Aleš Pultr, DrSc. (11.06.2019)
Oral exam. |
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Last update: prof. RNDr. Aleš Pultr, DrSc. (11.10.2017)
S. MacLane, Categories for Working Mathematician, Springer 1989. Appendix on categories in Picado-Pultr:Frames and Locales |
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Last update: prof. RNDr. Aleš Pultr, DrSc. (11.06.2019)
Categories and functors, examples. Natural transformations and natural equivalences. Special morphisms. Bounds, limits and colimits. Special (co)limits. Complete categories and theorems on completeness. Adjoint functors. Adjunction units. Adjunction and preserving limits or colimits. Theorem on the existence of adjoints. Yoneda lemma. Monads. Monads and adjunction. Description of algebraic structures (Eilenberg - Moore algebras). Kleisli categories; notes on their role in computer science. |
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Last update: prof. RNDr. Aleš Pultr, DrSc. (11.10.2017)
Basic concepts of category theory. Categories and functors, examples. Natural transformations and natural equivalences, examples. Special morphisms.
Basic categorial constructions. Factorisation. Image of a morphism. Bounds, limits and colimits. Special (co)limits. Complete categories and theorems on completeness.
Adjoint functors, examples. Descriptions of adjunctions by means of adjunction units, Reflective and coreflective subcategories. Adjunction and preserving limits or colimits. Theorem on the existence of adjoints.
Cartesian closed categories. Categories of functors.
Yoneda lemma. Categorical models of some theories.
Monads. Monads and adjunction. Description of algebraic structures (Eilenberg - Moore algebras). Kleisli categories; notes on their role in computer science. |