ScalingStacks

In Section 2 we set up notation for simplicial spaces and discuss the Reedy model category structure for simplicial spaces. In Section 3 we define the classification diagram construction, which produces a simplicial space from category theoretic data. In Section 4 we define the notion of a Segal space, and in Section 5 we discuss in elementary terms how one can view a Segal space as a model for a homotopy theory. In Section 6 we define the notion of a complete Segal space. In Section 7 we present our main theorems. In Section 8 we show how the classification diagram of a simplicial closed model category gives rise to a complete Segal space.

In Sections 9 through 14 we give proofs for the more technical results from earlier sections.