Discrete triangulated categories
Nathan Broomhead, David Pauksztello, David Ploog
TL;DR
This paper introduces new homological concepts that generalize discrete derived categories, demonstrating their applicability to Vossieck discrete algebras across all bounded t-structures and providing numerous examples.
Contribution
It develops generalized homological notions extending discrete derived categories and applies them to Vossieck discrete algebras with broad t-structure compatibility.
Findings
Vossieck discrete algebras possess the new property across all bounded t-structures
Multiple examples of triangulated categories are provided
New homological notions generalize existing discrete derived categories
Abstract
We introduce and study several homological notions which generalise the discrete derived categories of D. Vossieck. As an application, we show that Vossieck discrete algebras have this property with respect to all bounded t-structures. We give many examples of triangulated categories regarding these notions.
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