TL;DR
This paper proves the Koszulity of specific linear path categories derived from connected graphs with infinite directed walks, relating them to locally quadratic duals of preprojective algebras.
Contribution
It establishes the Koszulity of certain path categories associated with graphs, connecting them to quadratic duals of preprojective algebras.
Findings
Proves Koszulity for categories from graphs with infinite walks
Links these categories to locally quadratic duals of preprojective algebras
Provides new insights into the structure of path categories
Abstract
We prove Koszulity of certain linear path categories obtained from connected graphs with some infinite directed walk. These categories can be viewed as locally quadratic dual to preprojective algebras.
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