On Morita weak equivalences of simplicial algebraic theories and operads

Abstract

Generalizing a result of Dwyer and Kan for simplicial categories, we characterize the morphisms of multi-sorted simplicial algebraic theories and simplicial coloured operads which induce a Quillen equivalence between the corresponding categories of algebras.

21 pages. This paper contains Sections 4 and 5 of "Morita homotopy theory for $(\infty ,1)$-categories and $\infty$-operads" (arXiv:1707.06715v1), which have been removed from that paper and made a separate note. The updated version can be found in arXiv:1707.06715v2. v2: Final version