Cartesian closed category
Composition

Evaluating the exponential in one argument at a morphism p : X → Y gives morphisms

corresponding to the operation of composition with p. Alternate notations for the operation p include p and p∘-. Alternate notations for the operation Z include p and -∘p.

Evaluation maps can be chained as

the corresponding arrow under the exponential adjunction

is called the (internal) composition map.

In the particular case of the category Set, this is the ordinary composition operation:
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