Work

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

Year: 2023

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2304.02446

Author: Trnka, Dominik

Institutions: Czech Academy of Sciences, Masaryk University, Czech Academy of Sciences, Institute of Mathematics

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4362679518

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