Homotopy colimits of 2-functors

Homotopy (limits And) Colimits

These notes were written to accompany two talks given in the Algebraic Topology and Category Theory Proseminar at the University of Chicago in Winter 2009. When a category has some notion of limits and colimits associated to it, its ordinary limits and colimits are not necessarily homotopically meaningful. We describe a notion of a “homotopy colimit” for two sorts of categories with a homotopy ...

Colimits of Representable Algebra-valued Functors

If C and D are varieties of algebras in the sense of general algebra, then by a representable functor C → D we understand a functor which, when composed with the forgetful functor D → Set, gives a representable functor in the classical sense; Freyd showed that these functors are determined by D-coalgebra objects of C. Let Rep(C,D) denote the category of all such functors, a full subcategory of ...

Homotopy Fibre Sequences Induced by 2-functors

This paper contains some contributions to the study of the relationship between 2-categories and the homotopy types of their classifying spaces. Mainly, generalizations are given of both Quillen’s Theorem B and Thomason’s Homotopy Colimit Theorem to 2-functors. Mathematical Subject Classification: 18D05, 55P15, 18F25.

Homotopy colimits in model categories

A Primer on Homotopy Colimits