If there is a monoidal functor from a monoidal category M to a monoidal category N , then any category enriched over M can be reinterpreted as a ca...

Yoneda's lemma asserts that every natural transformation between Hom functors is of this form. In other words, the Hom functors give rise to a full...

Limits and universal morphisms Colimits in comma categories may be "inherited". If and are cocomplete, is a cocontinuous functor, and another funct...

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...

Some facts Every cyclic group is locally cyclic, and every locally cyclic group is abelian . Every finitely-generated locally cyclic group is cycli...

Every closed subgroup of a locally compact group is locally compact. (The closure condition is necessary as the group of rationals demonstrates.) C...

See finite morphism . The morphism f is locally of finite type if Y may be covered by affine open sets Spec B such that each inverse image f ? 1 (S...

Since straight regularity is a more familiar condition than either preregularity (which is usually weaker) or complete regularity (which is usually...