  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.
