Algebras of A PRO
An algebra of a PRO in a monoidal category is a strict monoidal functor from to . Every PRO and category give rise to a category of algebras whose objects are the algebras of in and whose morphisms are the natural transformations between them.
For example:
- an algebra of is just an object of ,
- an algebra of FinSet is a commutative monoid object of ,
- an algebra of is a monoid object in .
More precisely, what we mean here by "the algebras of in are the monoid objects in " for example is that the category of algebras of in is equivalent to the category of monoids in .
Read more about this topic: PRO (category Theory)
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