2-groupoid enrichments in homotopy theory and algebra (Q1611695)

This paper is a survey of the theory of categories enriched in \(2\)-categories or \(2\)-groupoids, using the tensor product of \(2\)-categories due to Gray. It describes several examples: the category of topological spaces; the category of \(2\)-groupoids itself; double deloopings of braided monoidal categories; the category of crossed \(2\)-complexes (which provides a model for homotopy \(3\)-types); the category of chain complexes; comma categories and diagram categories obtained from enriched categories. The treatment of chain complexes is particularly thorough and elementary.