An axiomatic approach for degenerations in triangulated categories
Manuel Saorin, Alexander Zimmermann (LAMFA)
TL;DR
This paper extends the concept of degeneration from Cohen Macaulay modules to objects in triangulated categories, establishing conditions under which different degeneration notions coincide.
Contribution
It introduces a new axiomatic framework for degenerations in triangulated categories, generalizing Yoshino's definition and linking it to distinguished triangles.
Findings
Degeneration notions are equivalent under certain natural conditions.
The framework generalizes existing module degeneration concepts.
Provides a characterization similar to Zwara's in module varieties.
Abstract
We generalise Yoshino's definition of a degeneration of two Cohen Macaulay modules to a definition of degeneration between two objects in a triangulated category. We derive some natural properties for the triangulated category and the degeneration under which the Yoshino-style degeneration is equivalent to the degeneration defined by a specific distinguished triangle analogous to Zwara's characterisation of degeneration in module varieties.
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