# mathlibdocumentation

category_theory.monoidal.End

# Endofunctors as a monoidal category. #

We give the monoidal category structure on C ⥤ C, and show that when C itself is monoidal, it embeds via a monoidal functor into C ⥤ C.

## TODO #

Can we use this to show coherence results, e.g. a cheap proof that λ_ (𝟙_ C) = ρ_ (𝟙_ C)? I suspect this is harder than is usually made out.

The category of endofunctors of any category is a monoidal category, with tensor product given by composition of functors (and horizontal composition of natural transformations).

Equations

Tensoring on the right gives a monoidal functor from C into endofunctors of C.

Equations
@[simp]
@[simp]