2021/07/21 by Blom, Thomas, Moerdijk, Ieke · 1 citation
#18M60 #18M75 #18N40 #18N60 #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2107.10092
We show that a profinite completion functor for (simplicial or topological) operads with good homotopical properties can be constructed as a left Quillen functor from an appropriate model category of infinity-operads to a certain model category of profinite infinity-operads. The construction is based on a notion of lean infinity-operad, and we characterize those infinity-operads weakly equivalent to lean ones in terms of homotopical finiteness properties. Several variants of the construction are also discussed, such as the cases of unital (or closed) infinity-operads and of infinity-categories.