Deformations of homotopy theories via algebraic theories

Abstract

We develop a homotopical variant of the classic notion of an algebraic theory as a tool for producing deformations of homotopy theories. From this, we extract a framework for constructing and reasoning with obstruction theories and spectral sequences that compute homotopical data starting with purely algebraic data.

59 pages. v2: added section on the spiral spectral sequence. v3: many small improvements; accepted version, to appear in Advances in Mathematics