It is an old observation of Eckmann-Hilton [21], that the homotopy theory of topological
spaces has an algebraic analogue in the module category of a ring. Inspired by the work of …

Recall that a module X over some associative ring R is endofinite if X has finite length when
viewed as a module over its endomorphism ring EndR (X). Such modules have been …

Let R be a ring. We prove that the homotopy category K (R-Proj) is always \aleph_1-
compactly generated, and, depending on the ring R, it may or may not be compactly …

The homotopy category of complexes of projective modules Page 1 Advances in Mathematics
193 (2005) 223–232 www.elsevier.com/locate/aim The homotopy category of complexes of …

The concept of homotopy for homomorphisms of modules, suggested by analogy with
fundamental properties of the topological homotopy, was developed by Eckmann and Hilton …

Quillen [35] from a category C, usually the category of simplicial sets or of chain complexes
over some ring, to give a homotopy theory or homo-topical algebra in pro (C).(It is worth …

It is shown that the category of enriched functors [C, V] is Grothendieck whenever V is a
closed symmetric monoidal Grothendieck category and C is a category enriched over V …

The homotopy groups of topological spaces have been generalized by Eckmann-Hilton to
two-space homotopy groups IIn (X, Y) that contain homotopy groups and cohomology …

We develop in this paper the stable theory for projective complexes, by which we mean to
consider a chain complex of finitely generated projective modules as an object of the factor …

Under suitable assumptions, we extend the inclusion of an additive subcategory\raise0. 3em
\scriptscriptstyle- X ⊂\raise0. 3em \scriptscriptstyle- A (= stable category of an exact category …