Category-colored Operads, Internal Operads, and Markl $\mathbb{O}$-operads

Dominik Trnka

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arXiv · 2304.02446

Category-colored Operads, Internal Operads, and Markl $\mathbb{O}$-operads

Dominik Trnka

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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.

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Dominik Trnka. 2023-04-05. Category-colored Operads, Internal Operads, and Markl $\mathbb{O}$-operads. https://arxiv.org/abs/2304.02446

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