Stage item

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PROP.

Last seen on: –Thomas Joseph – King Feature Syndicate Crossword – Jun 22 2022
USA Today Crossword – Dec 16 2019

Random information on the term “PROP”:

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 { 0 , 1 , … , n − 1 } {\displaystyle \{0,1,\ldots ,n-1\}} 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 Broadman and Vogt. Following them, J. P. May then introduced the notion of “operad”.

There are the following inclusions of full subcategories:

where the first category is the category of (symmetric) operads.

PROP on Wikipedia