Absolutely Clean, Level, and Gorenstein AC-Injective Complexes
Daniel Bravo, James Gillespie

TL;DR
This paper extends the concepts of absolutely clean, level, and Gorenstein AC-injective modules to chain complexes, establishing model structures where Gorenstein AC-injective complexes are fibrant objects.
Contribution
It introduces and characterizes Gorenstein AC-injective and projective complexes, and constructs a cofibrantly generated model structure on chain complexes with these as fibrant objects.
Findings
Gorenstein AC-injective complexes characterized in chain complexes
A model structure on chain complexes with Gorenstein AC-injective complexes as fibrant objects
Extension of Gorenstein homological algebra to chain complexes
Abstract
Absolutely clean and level -modules were introduced in [BGH13] and used to show how Gorenstein homological algebra can be extended to an arbitrary ring . This led to the notion of Gorenstein AC-injective and Gorenstein AC-projective -modules. Here we study these concepts in the category of chain complexes of -modules. We define, characterize and deduce properties of absolutely clean, level, Gorenstein AC-injective, and Gorenstein AC-projective chain complexes. We show that the category of chain complexes has a cofibrantly generated model structure where every object is cofibrant and the fibrant objects are exactly the Gorenstein AC-injective chain complexes.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Commutative Algebra and Its Applications
