The Auslander–Reiten Theory of the Morphism Category of Projective Modules

Abstract

We investigate certain almost split sequences in the category of morphisms between projective modules over an Artin algebra. This category has interesting properties and is closely linked to

\tau

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-tilting theory and the Auslander–Reiten theory of the module category. We give an explicit description of particular almost split sequences that begin or end at specific objects, and discuss applications, including their connection to g-vectors.

Keywords

Morphism category / Almost split sequence / Cokernel functor / g-vector / 18A20 / 16G70 / 16G10

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