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Category-colored Operads, Internal Operads, and Markl $\mathbb{O}$-operads (2304.02446v2)
Published 5 Apr 2023 in math.CT and math.AT
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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