Homotopy for functors

Rational Homotopy Calculus of Functors

of “Rational Homotopy Calculus of Functors” by Ben C. Walter, Ph.D., Brown University, July 2005. We construct a homotopy calculus of functors in the sense of Goodwillie for the categories of rational homotopy theory. More precisely, given a homotopy functor between any of the categories of differential graded vector spaces (DG), reduced differential graded vector spaces, differential graded Li...

Coherent Functors in Stable Homotopy Theory

such that C and D are compact objects in S (an object X in S is compact if the representable functor Hom(X,−) preserves arbitrary coproducts). The concept of a coherent functor has been introduced explicitly for abelian categories by Auslander [1], but it is also implicit in the work of Freyd on stable homotopy [9]. In this paper we characterize coherent functors in a number of ways and use the...

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.

Change of universe functors in equivariant stable homotopy theory

One striking difference between nonequivariant and equivariant stable homotopy is that, in the equivariant context, one must specify those representations with respect to which spectra are to be stable. One may specify stability with respect only to trivial representations (thereby obtaining what is often called the naive equivariant stable category), with respect to all representations (thereb...

Investigation of Concurrent Processes by Means of Homotopy Functors