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About this paper
Samuel Mimram, Cinzia Di Giusto
This paper presents a categorical theory for version control systems, modeling files as objects and patches as morphisms where merging corresponds to categorical pushouts. It constructs a new category whose objects are defined as finite sets with a transitive relation and labels, enabling the formal representation and resolution of all merge operations, including those arising from conflicting patches.
Key insights
- The absence of a pushout for coinitial patches in the initial category \(\mathcal{L}\) is identified as the mathematical representation of a conflict between modifications.
- By completing \(\mathcal{L}\) to a finitely cocomplete category \(\mathcal{P}\), all merge scenarios, including conflicting ones, are guaranteed to have a well-defined categorical pushout, providing a robust model for conflict representation.
- The resulting objects in \(\mathcal{P}\) with partially ordered lines formally represent files in conflicting states, where different concurrent modifications or unresolved choices exist.
Summary by alphaXiv.
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