On Morita weak equivalences of simplicial algebraic theories and operads

TL;DR

This paper characterizes morphisms between simplicial algebraic theories and operads that lead to equivalent categories of algebras, extending known results from simplicial categories to more complex structures.

Contribution

It generalizes Dwyer and Kan's result to multi-sorted theories and operads, providing criteria for Quillen equivalences in these contexts.

Findings

Identifies conditions for Quillen equivalences between algebra categories

Extends known theory from simplicial categories to algebraic theories and operads

Provides a framework for understanding morphisms inducing equivalences

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.