PlanetPhysics/Enriched Category Theory

Enriched Category Theory
This is a new, contributed topic on enrichments of category theory, including a weak Yoneda lemma, functor categories, 2-categories and representable V-functors.

Monoidal Categories
$$2-category$$ VCAT for a monoidal V category $$2-functors$$, such as $$F: VCAT \to CAT$$

Tensor products and duality Closed and bi-closed bimonoidal categories

Representable V 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 isomorphism $$[A \times [B, C]] \cong [A,[B,C]]$$

Indexed limits and colimits
Indexing 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