Truncated operads and simplicial spaces

Abstract

It was shown by Boavida de Brito and Weiss (J. Topol. 11:1 (2018), 65–143) that a well-known construction which to a (monochromatic, symmetric) topological operad associates a topological category and a functor from it to the category of finite sets is homotopically fully faithful, under mild conditions on the operads. The main result here is a generalization of that statement to $k$-truncated topological operads. A $k$-truncated operad is a weaker version of operad where all operations have arity $\le k$.