English

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.

Keywords

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

R2 v1 2026-06-23T04:09:01.954Z