Enriched functor

In category theory, an enriched functor is a variant on a special type of mapping between categories.

Definition

A functor T is said to be C-enriched if for all objects X and Y in C, there are arrows

<math>tXY:(X \rightarrow Y) \longrightarrow (TX \rightarrow TY)<math>

satisfying

<math>tXX(\mathrm{id}(X)) = \mathrm{id}(TX)\,<math>

for all X in C, and

<math>tXY(f) \circ tYZ(g) = tXZ(f \circ g)<math>

for all f: X → Y and g: Y → Z in C.

References

• [Ke] Kelly,G.M. "Basic Concepts of Enriched Category Theory", London
• Mathematical Society Lecture Note Series No.64 (C.U.P., 1982)

External links

• An extension of Reynolds' result on the non-existence of set-models of polymorphism
• Semantics for Algebraic Operations