Abstract
The category of (colored) props is an enhancement of the category of colored operads, and thus of the category of small categories. The titular category has nice formal properties: it is bicomplete and is a symmetric monoidal category, with monoidal product closely related to the Boardman-Vogt tensor product of operads. Tools developed in this article, which is the first part of a larger work, include a generalized version of multilinearity of functors, a free prop construction defined on certain “generalized” graphs, and the relationship between the category of props and the categories of permutative categories and of operads.
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Hackney, P., Robertson, M. On the Category of Props. Appl Categor Struct 23, 543–573 (2015). https://doi.org/10.1007/s10485-014-9369-4
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DOI: https://doi.org/10.1007/s10485-014-9369-4