The identity morphism in a monoidal category corresponds to the unit element

The unit element defined for a set-theory monoid corresponds to the identity morphism within a monoidal category.

Because the composition of morphisms in a monoidal category corresponds to an associative binary operation and composition with the identity morphism conforms to the law of identity, the unit element being used as an operand in the associative binary operation is the same thing as composition with the identity morphism.

Backlinks

• A set-theory monoid and a category-theory monoid are the same thing
  • Similarly, the identity morphism in a monoidal category corresponds to the unit element
• A monoid has a unit element
  • The identity morphism in a monoidal category corresponds to the unit element