Category-colored operads, internal operads, and Markl O-operads

Dominik Trnka

We present a Markl-style definition of operads colored by a small category. In the presence of a unit these are equivalent to substitudes of Day and Street. We show that operads colored by a category are internal algebras of a certain categorical operad of functors. We describe a groupoid-colored quadratic binary operad, whose algebras are non-unital Markl operads in the context of operadic categories. As a by-product we describe the free internal operad construction.

Keywords: Colored operad, Internal operad, Operadic category, Markl operad, Hyperoperad

2020 MSC: 18M60

Theory and Applications of Categories, Vol. 39, 2023, No. 30, pp 874-915.

Published 2023-11-13.

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