Introduction to Abelian Model Structures and Gorenstein Homological Dimensions

The first part of the book introduces the definitions and notations
of the universal constructions most often used in category theory. The
next part presents a proof of the Eklof and Trlifaj theorem in
Grothedieck categories and covers M. Hovey’s work that connects the
theories of cotorsion pairs and model categories. The final two parts
study the relationship between model structures and classical and
Gorenstein homological dimensions and explore special types of
Grothendieck categories known as Gorenstein categories.

As self-contained as possible, this book presents new results in
relative homological algebra and model category theory. The author also
re-proves some established results using different arguments or from a
pedagogical point of view. In addition, he proves folklore results that
are difficult to locate in the literature.