Support, with "up"

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Possible Answers: PROP, SHORE.

Random information on the term “PROP”:

In category theory, a PRO is a strict monoidal category whose objects are the natural numbers (including zero), and whose tensor product is given on objects by the addition on numbers.

Some examples of PROs:

The name PRO is an abbreviation of “PROduct category”. PROBs and PROPs are defined similarly with the additional requirement for the category to be braided, and to have a symmetry (that is, a permutation), respectively. All of the examples above are PROPs, except for the simplex category and BijBraid; the latter is a PROB but not a PROP, and the former is not even a PROB.

An algebra of a PRO

P

{\displaystyle P}

in a monoidal category

C

{\displaystyle C}

is a strict monoidal functor from

P

{\displaystyle P}

to

C

{\displaystyle C}

. Every PRO

P

{\displaystyle P}

and category

C

{\displaystyle C}

give rise to a category

A
l
g

P

C

{\displaystyle \mathrm {Alg} _{P}^{C}}

of algebras whose objects are the algebras of

P

{\displaystyle P}

in

C

{\displaystyle C}

and whose morphisms are the natural transformations between them.

PROP on Wikipedia

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