Problems formulated with adjoint functors 1.3 Adjoint functors as solving optimization problems 1.4 The case of partial orders 2 Formal definitions...

Preservation of limits Representable functors are naturally isomorphic to Hom functors and therefore share their properties. In particular, (covari...

Beck's monadicity theorem gives a characterization of monadic functors. [ edit ] Uses Monads are used in functional programming to express types of...

Ab is a reflective subcategory of the category of groups , Grp . The reflector is the functor which sends each group to its abelianization . Simila...

The smash product of any pointed space X with a 0-sphere is homeomorphic to X . The smash product of two circles is a quotient of the torus homeomo...

F and a subset A of E . Let be the family of all finite subsets of A then . In other words the adjunction of any set can be reduced to a union of a...

Complete Heyting algebras arise as the Lindenbaum algebras of (intuitionistic) logics with infinite disjunction. [ edit ] Frames and locales The ob...

Group algebra over a finite group 4.1 Regular representation 4.2 Properties 4.3 Representations of a group algebra 4.4 Center of a group algebra 5 ...

Distinction with symmetric tensors The symmetric algebra and symmetric tensors are easily confused: the symmetric algebra is a quotient of the tens...