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Applied Categorical Structures

, Volume 23, Issue 4, pp 543–573 | Cite as

On the Category of Props

  • Philip Hackney
  • Marcy Robertson
Article
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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.

Keywords

Colored operad Colored prop Multicategory Permutative category 
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© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California-RiversideRiversideUSA
  2. 2.Department of MathematicsUniversity of Western OntarioLondonCanada

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