mathlib documentation

category_theory.closed.monoidal

Closed monoidal categories #

Define (right) closed objects and (right) closed monoidal categories.

TODO #

Some of the theorems proved about cartesian closed categories should be generalised and moved to this file.

@[class]

An object X is (right) closed if (X ⊗ -) is a left adjoint.

Instances of this typeclass
Instances of other typeclasses for category_theory.closed
  • category_theory.closed.has_sizeof_inst
@[class]

A monoidal category C is (right) monoidal closed if every object is (right) closed.

Instances of this typeclass
Instances of other typeclasses for category_theory.monoidal_closed
  • category_theory.monoidal_closed.has_sizeof_inst

The unit object is always closed. This isn't an instance because most of the time we'll prove closedness for all objects at once, rather than just for this one.

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