Monoidal categories

PROP (category theory)

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. (Wikipedia).

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From playlist Category Theory

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From playlist Category Theory course

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From playlist Category Theory

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From playlist Category Theory

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From playlist SMRI Seminars

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From playlist Global Noncommutative Geometry Seminar (Asia and Pacific)

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From playlist Mathematics

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From playlist Category Theory: The Beginner’s Introduction

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From playlist Academic Talks

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From playlist Category Theory: The Beginner’s Introduction

Related pages

Monoidal functor | Block matrix | Discrete category | Braided monoidal category | Identity matrix | Symmetric monoidal category | Symmetric group | FinSet | Lawvere theory | Braid group | Base (exponentiation) | Equivalence of categories | Category theory | Simplex category | Kronecker product | Automorphism group | Matrix multiplication | Monoidal category | Permutation category | Operad