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9781498725347

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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

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Dr. Marco A. Pérez is a postdoctoral fellow at the Mathematics Institute of the Universidad Nacional Autónoma de México, where he works on Auslander–Buchweitz approximation theory and cotorsion pairs. He was previously a postdoctoral associate at the Massachusetts Institute of Technology, working on category theory applied to communications and linguistics. Dr. Pérez’s research interests cover topics in both category theory and homological algebra, such as model category theory, ontologies, homological dimensions, Gorenstein homological algebra, finitely presented modules, modules over rings with many objects, and cotorsion theories. He received his PhD in mathematics from the Université du Québec à Montréal in the spring of 2014.

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