Fuzzy Presheaves are Quasitoposes

Aloïs Rosset*, Roy Overbeek, Jörg Endrullis

*Corresponding author for this work

Research output: Chapter in Book / Report / Conference proceedingConference contributionAcademicpeer-review


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 graph categories are quasitoposes.

Original languageEnglish
Title of host publicationGraph Transformation
Subtitle of host publication16th International Conference, ICGT 2023, Held as Part of STAF 2023, Leicester, UK, July 19–20, 2023, Proceedings
EditorsMaribel Fernández, Christopher M. Poskitt
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages21
ISBN (Electronic)9783031367090
ISBN (Print)9783031367083
Publication statusPublished - 2023
Event16th International Conference on Graph Transformation, ICGT 2023 - Leicester, United Kingdom
Duration: 19 Jul 202320 Jul 2023

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13961 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference16th International Conference on Graph Transformation, ICGT 2023
Country/TerritoryUnited Kingdom

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.


  • Fuzzy set
  • Graph rewriting
  • Presheaf
  • Quasitopos


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