Expansions of abelian categories
Xiao-Wu Chen, Henning Krause
TL;DR
This paper introduces the concept of expansions of abelian categories, a new functorial tool that aids in induction and reduction, with applications in the study of coherent sheaves on weighted projective lines.
Contribution
It defines and explores expansions of abelian categories, providing a new framework for related mathematical arguments and applications.
Findings
Introduces the concept of expansions of abelian categories
Demonstrates applications in coherent sheaves on weighted projective lines
Provides tools for induction and reduction in category theory
Abstract
Expansions of abelian categories are introduced. These are certain functors between abelian categories and provide a tool for induction/reduction arguments. Expansions arise naturally in the study of coherent sheaves on weighted projective lines; this is illustrated by various applications.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Algebraic Geometry and Number Theory · Nonlinear Waves and Solitons