From Γ-spaces to algebraic theories

Abstract

The paper examines semi-theories, that is, formalisms of the type of the Γ \Gamma -spaces of Segal which describe homotopy structures on topological spaces. It is shown that for any semi-theory one can find an algebraic theory describing the same structure on spaces as the original semi-theory. As a consequence one obtains a criterion for establishing when two semi-theories describe equivalent homotopy structures.