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arXiv · 2301.13067

Fuzzy Presheaves are Quasitoposes

Aloïs Rosset·Roy Overbeek·Jörg Endrullis
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Abstract

Quasitoposes encompass a wide range of structures, including various categories of graphs. They have proven to be a natural setting for reasoning about the metatheory of algebraic graph rewriting. In this paper we propose and motivate the notion of fuzzy presheaves, which generalises fuzzy sets and fuzzy graphs. We prove that fuzzy presheaves are rm-adhesive quasitoposes, proving our recent conjecture for fuzzy graphs. Furthermore, we show that simple fuzzy graphs categories are quasitoposes.

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Aloïs Rosset, Roy Overbeek, Jörg Endrullis. 2023-01-30. Fuzzy Presheaves are Quasitoposes. https://arxiv.org/abs/2301.13067

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