let r be a commutative noetherian ring. we study the behavior of injectiveand at dimension of r-modules under the functors homr(-,-) and -×r-.

In order to solve domain equations over 1-bounded compact metric spaces, xed points of functors on categories of 1-bounded compact metric spaces are studied. Two categories of 1-bounded compact metric spaces are considered: KMS and KMS E. In both categories, objects are isomorphic if and only if they are isometric. As a consequence, provided that the operation of a domain equation can be extend...

iv Contents Preface vii Chapter 1. Model categories 1 1.1. The definition of a model category 2 1.2. The homotopy category 7 1.3. Quillen functors and derived functors 13 1.3.1. Quillen functors 13 1.3.2. Derived functors and naturality 16 1.3.3. Quillen equivalences 19 1.4. 2-categories and pseudo-2-functors 22 Chapter 2. Examples 27 2.1. Cofibrantly generated model categories 28 2.1.1. Ordina...

The adjoint representation of a simple Lie algebra g admits a deformation into an irreducible representation R of the quantum group Uq(g). In this paper for a simply-laced g we realize R as the Grothendieck group of a particular abelian category C. There are exact functors from C to C which on the Grothendieck group act as the quantum group generators Eα, Fα, where α varies over simple roots. V...