Geodesic
Category-colored operads, internal operads, and Markl O-operads
Theory and applications of categories, Tome 39 (2023), pp. 874-915.

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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.
Publié le :
Classification : 18M60
Keywords: Colored operad, Internal operad, Operadic category, Markl operad, Hyperoperad 
@article{TAC_2023_39_a29,
     author = {Dominik Trnka},
     title = {Category-colored operads, internal operads, and {Markl} {O-operads}},
     journal = {Theory and applications of categories},
     pages = {874--915},
     publisher = {mathdoc},
     volume = {39},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2023_39_a29/}
}
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Dominik Trnka. Category-colored operads, internal operads, and Markl O-operads. Theory and applications of categories, Tome 39 (2023), pp. 874-915. http://geodesic.mathdoc.fr/item/TAC_2023_39_a29/