Derived category of weak chain ๐ฐ-complexes
Fajar Yuliawan, Intan Muchtadi-Alamsyah, Valerian Pratama, Gustina Elfiyanti
TL;DR
This paper introduces and characterizes the derived category of weak chain U-complexes and establishes a natural isomorphism with homology functors.
Contribution
The paper introduces a new derived category for weak chain U-complexes and establishes a novel natural isomorphism via an adjoint pair.
Findings
A derived category of weak chain U-complexes is defined and characterized.
An adjoint pair is constructed between chain complexes and weak chain U-complexes.
The homology functor is shown to be a natural isomorphism.
Abstract
In this paper, we define the derived category of weak chain U-complexes, and we give a characterization of any weak chain U-complex as an object in the right bounded homotopy category of weak chain U-complexes of projective modules. Then, we show that the homology functor between the category of chain complexes and weak chain U-complexes is a natural isomorphism by constructing an adjoint pair between these two categories.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology