PlanetPhysics/Enriched Category Theory

Enriched Category Theory

This is a new, contributed topic on enrichments of [[../TrivialGroupoid/|category theory]], including a weak [[../AbelianCategoryEquivalenceLemma/|Yoneda lemma]], [[../TrivialGroupoid/|functor categories]], [[../2Category2/|2-categories]] and representable V-functors.

Monoidal Categories

$2-category$ VCAT for a monoidal V [[../Cod/|category]] $2-functors$, such as $F:VCAT\to CAT$

[[../Tensor/|Tensor]] products and [[../DualityAndTriality/|duality]] Closed and bi-closed bimonoidal categories

Representable V [[../TrivialGroupoid/|functors]] Extraordinary V naturality and the V naturality of the canonical maps

Universe enlargement $V\to enV$ : consider $[A,B]$ as an enV category

The [[../IsomorphicObjectsUnderAnIsomorphism/|isomorphism]] $[A\times [B,C]]\cong [A,[B,C]]$

Indexed limits and colimits

Indexing [[../Bijective/|types]]; limits and colimits; Yoneda isomorphisms

Preservation of limits and colimits

Limits in functor categories: double limits and iterated limits

The connection with classical conical limits when $V=Set$

Kan extensions

The definition of Kan extensions: their expressibility by limits and colimits

Functor categories, small Projective Limits and Morita Equivalence

more to come