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...

If the diagram is contravariant then it is called an inverse system . [ edit ] Cones and limits A cone of a diagram D  : J ? C is a morphism from t...

It follows that any functor which preserves limits will take terminal objects to terminal objects, and any functor which preserves colimits will ta...

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...

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...

Zero morphism - Wikipedia, the free encyclopedia Zero morphism From Wikipedia, the free encyclopedia Jump to: navigation , search In category theor...

Then the equaliser is again the entire domain X , since the universal quantification in the definition is vacuously true . [ edit ] Difference kern...

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...

Subobject classifier - Wikipedia, the free encyclopedia Subobject classifier From Wikipedia, the free encyclopedia Jump to: navigation , search In ...

Commutativity makes sense for a polygon of any finite number of sides (including just 1 or 2), and a diagram is commutative if every polygonal subd...

Snake lemma - Wikipedia, the free encyclopedia Snake lemma From Wikipedia, the free encyclopedia Jump to: navigation , search In mathematics , part...