The aim of this paper is two-fold. First, we compare two notions of a "space" of algebra structures over an operad A: 1. the classification space, which is the nerve of the category of weak equivalences of A-algebras, and 2. the moduli space A{X}, which is the space of maps from A to the endomorphism operad of an object X. We show that under certain hypotheses the moduli space of A-algebra stru...
