Frobenius quotients, inflation categories and weighted projective lines

TL;DR

The paper introduces Frobenius quotients between categories, showing how they induce quotients between inflation categories, with an explicit example involving vector bundles on weighted projective lines.

Contribution

It defines Frobenius quotients between Frobenius exact categories and demonstrates their effect on inflation categories, providing an explicit example with weighted projective lines.

Findings

Frobenius quotients induce quotients between inflation categories

Explicit Frobenius quotient constructed from vector bundles on weighted projective lines

Categories of monomorphism grids derived from weighted projective lines

Abstract

We propose the notion of Frobenius quotients between Frobenius exact categories. It turns out that any Frobenius quotient induces Frobenius quotients between the corresponding inflation categories. We obtain an explicit Frobenius quotient from the category of vector bundles on weighted projective lines with three weights to a certain category consisting of monomorphism grids.