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PROP.
Last seen on: The Guardian – Cryptic Crossword No 28,836 – Aug 15 2022s
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 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.