Category-colored Operads, Internal Operads, and Markl $\mathbb{O}$-operads
Category Theory
2023-11-21 v2 Algebraic Topology
Abstract
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
Cite
@article{arxiv.2304.02446,
title = {Category-colored Operads, Internal Operads, and Markl $\mathbb{O}$-operads},
author = {Dominik Trnka},
journal= {arXiv preprint arXiv:2304.02446},
year = {2023}
}