Description
Book SynopsisIntroduction to Abelian Model Structures and Gorenstein Homological Dimensions provides a starting point to study the relationship between homological and homotopical algebra, a very active branch of mathematics. The book shows how to obtain new model structures in homological algebra by constructing a pair of compatible complete cotorsion pairs related to a specific homological dimension and then applying the Hovey Correspondence to generate an abelian model structure.
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 categorie
Trade Review
"This book is a worthy addition to the relative homological algebra literature. Graduate students can use it to introduce themselves in the topic and it is also a useful reference's book for specialists in the field of homological algebra."
- Blas Torrecillas
"The main goal of this book is to provide a multitude of model category structures for categories such as categories of chain complexes, categories of modules, and more specifically, Gorenstein categories (a Grothendieck category with extra properties). The author provides these model category structures by making use of the Hovey Correspondence, which allows one to associate a model category structure to a complete cotorsion pair in an abelian category […]
This text is based on the thesis of the author and the majority of original results presented here are related to the model category structures coming from homological dimensions. The intended audience includes graduate students pursuing a degree in the field and researchers interested in the development of model category structures associated to Gorenstein homological dimensions. It is well written and is well suited for the target audience."
- Bruce R. Corrigan-Salter, Mathematical Reviews, August 2017
"The main goal of this book is to provide a multitude of model category structures for categories such as categories of chain complexes, categories of modules, and more specifically, Gorenstein categories (a Grothendieck category with extra properties). The author provides these model category structures by making use of the Hovey Correspondence, which allows one to associate a model category structure to a complete cotorsion pair in an abelian category […]
This text is based on the thesis of the author and the majority of original results presented here are related to the model category structures coming from homological dimensions. The intended audience includes graduate students pursuing a degree in the field and researchers interested in the development of model category structures associated to Gorenstein homological dimensions. It is well written and is well suited for the target audience."
- Bruce R. Corrigan-Salter, Mathematical Reviews, August 2017
Table of ContentsCategorical and algebraic preliminaries. Interactions between homological algebra and homotopy theory. Classical homological dimensions and abelian model structures on chain complexes. Gorenstein homological dimensions and abelian model structures. Bibliography. Index.
