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

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Authors

TRNKA Dominik

Year of publication 2023
Type Article in Periodical
Magazine / Source Theory and Applications of Categories
MU Faculty or unit

Faculty of Science

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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