Properads

# Properads

## Definition

A properad in a symmetric monoidal category $C$ is a monoid in the monoidal category of bisymmetric sequences in $C$ (i.e., functors $\Sigma\times\Sigma\to C$) equipped with a version of substitution product modeled on connected directed graphs with 2 levels instead of corollas, which are used for operads. See §1.2 in Vallette [1] for details. The idea is that operations in a properad can have multiple inputs and outputs, as opposed to a single output in an operad. On the other hand, a properad is less general than a prop, because a prop also allows nonconnected graphs in the definition of the substitution product.

## References

Last revised on July 21, 2016 at 20:46:55. See the history of this page for a list of all contributions to it.