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 generated. …

… the homotopy category of injectives, the central object of this paper is the homotopy category
Kac(… calls the (injective) stable derived category of A1. The relationship between these two …

… To define Rf∗ of an object in D(X), one expresses the derived category D(X) as a quotient
of the the homotopy category K(X) by the acyclic complexes E(X), and notes that the …

… properly, Quillen axiomatized the usual construction of the homotopy category of spaces, …
We examine the definition of duality functors on the category of dg-modules M = dg Mod, of …

… Global “geometric” class field theory as a cohomological duality formula. Serre duality and …
a category equivalent to the usual homotopy category (Hot). Thus we get a composed functor …

… homotopy category … Grothendieck duality theorem. Furthermore, we prove that D ⊗• OX
induces an equivalence between the pure derived category of flats and the pure derived category …

… Indeed, Grothendieck defines the homotopy category Hot of CW-complexes in [11] as the …
This leads Grothendieck to an axiomatization of the class of weak equivalence in Cat, that …

… of the field with one element”) is the stable homotopy category of connective spectra. We
also describe some basic features of Grothendieck duality for the map from Spec Z to Spec M0, …

… abstract foundations of Grothendieck Duality—existence and … are proved, including
Grothendieck duality for proper morphisms, … and these maps depend only on the homotopy class …

… additive functor from the abelian category of OX -modules to the abelian category of OY -modules,
that extends in the obvious way to the respective homotopy categories K(X) and K(Y ): …