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

Universal cones Limits and colimits are defined as universal cones . That is, cones through which all other cones factor. A cone ? from L to F is a...

It follows that if coproducts exists in a given category (they need not) they are unique up to a unique isomorphism that respects the injections. I...

Set (with the monoidal structure induced by the cartesian product) is a monoid in the usual sense. A monoid object in Top (with the monoidal struct...

B , the pullback X × B E is a fiber bundle over X called the pullback bundle . The associated commutative diagram is a morphism of fiber bundles. I...