Category-colored operads, internal operads, and Markl O-operads
| Authors | |
|---|---|
| Year of publication | 2023 |
| Type | Article in Periodical |
| Magazine / Source | Theory and Applications of Categories |
| MU Faculty or unit | |
| Citation | |
| Web | http://www.tac.mta.ca/tac/volumes/39/30/39-30abs.html |
| Keywords | Colored operad; Internal operad; Operadic category; Markl operad; Hyperoperad |
| Description | 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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