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A model for the homotopy theory of homotopy theory. (English) Zbl 0961.18008
D. G. Quillen’s motivation for closed model categories [“Homotopical algebra”, Lect. Notes Math. 43 (1967; Zbl 0168.20903)] is to show criteria which would imply that two models give rise to equivalent homotopy theories.
The author studies a model for a homotopy theory, called a complete Segal space. Then such a space is itself an object in a certain Quillen closed model category and the category of those spaces has a well-behaved internal hom-object.

MSC:
18G30 Simplicial sets; simplicial objects in a category (MSC2010)
55U35 Abstract and axiomatic homotopy theory in algebraic topology
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