Dwyer--Kan homotopy theory for cyclic operads
Algebraic Topology
2023-12-14 v3 Category Theory
Quantum Algebra
Abstract
We introduce a general definition for colored cyclic operads over a symmetric monoidal ground category, which has several appealing features. The forgetful functor from colored cyclic operads to colored operads has both adjoints, each of which is relatively simple. Explicit formulae for these adjoints allow us to lift the Cisinski--Moerdijk model structure on the category of colored operads enriched in simplicial sets to the category of colored cyclic operads enriched in simplicial sets.
Cite
@article{arxiv.1809.06322,
title = {Dwyer--Kan homotopy theory for cyclic operads},
author = {Gabriel C. Drummond-Cole and Philip Hackney},
journal= {arXiv preprint arXiv:1809.06322},
year = {2023}
}
Comments
v3: updated numbering of theorem-like environments, subsections, and equations to reflect those in published version. no other changes. v2: final version, four figures added