Syllabus
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.
Annotation
Basic notions of category theory: category, functor, transformation. Categorial constructions, in particular limits and colimits.
Adjunction and preserving (co)limits. Monads, description of algebras, Kleisli categories.