Monoid (category theory)

Monoid object is in category theory is a generalization of the notion of monoid.

Definition

It was a monoidale category with the functor, the unit object of natural transformation with components, as well as the natural transformations and where.

A monoid object is now an object with two arrows, and, for the equations

  • ,
  • And

. apply

Examples

  • Monoids are Monoidobjekte in the category of sets, which is monoidal with the Cartesian product.
  • Group objects are Monoidobjekte.
  • In the category of monoids ( monoidal by direct products ) monoid objects are commutative monoids.
  • Is any category, then the functor category with the Funktorkomposition is monoidal. Monoid objects are monads.
Monoidal category Monad (category theory)
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