Finite-sum conjecture for morphisms between sheet modules

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A sheet module is the image of a decorous submodule in a decorous quotient of a representable projective, as defined in the paper. The elementary and multi-elementary morphisms are the morphisms between sheet modules introduced by analyzing images of generators and combining elementary morphisms. Finite-sum conjecture. Every morphism between sheet modules is a finite sum of multi-elementary morphisms. This conjecture proposes a complete description of morphisms between sheet modules in terms of the elementary constructions developed in the paper; its status is not resolved in the supplied text.

References

Primary source

Job Daisie Rock and Hugh Thomas, “Preprojective categories of type A”, arXiv:2512.09618 (2025).

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