PROP (category theory)

rdf:langString PROP (category theory)

rdf:langString In category theory, a branch of mathematics, a PROP is a symmetric strict monoidal category whose objects are the natural numbers n identified with the finite sets and whose tensor product is given on objects by the addition on numbers. Because of “symmetric”, for each n, the symmetric group on n letters is given as a subgroup of the automorphism group of n. The name PROP is an abbreviation of "PROduct and Permutation category". The notion was introduced by Adams and MacLane; the topological version of it was later given by Boardman and Vogt. Following them, J. P. May then introduced the notion of “operad”, a particular kind of PROP. There are the following inclusions of full subcategories: where the first category is the category of (symmetric) operads.