Fuzzy Presheaves are Quasitoposes

Aloïs Rosset; Roy Overbeek; Jörg Endrullis

doi:10.1007/978-3-031-36709-0_6

Fuzzy Presheaves are Quasitoposes

Aloïs Rosset^*, Roy Overbeek, Jörg Endrullis

^*Corresponding author for this work

Research output: Chapter in Book / Report / Conference proceeding › Conference contribution › Academic › peer-review

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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 graph categories are quasitoposes.

Original language	English
Title of host publication	Graph Transformation
Subtitle of host publication	16th International Conference, ICGT 2023, Held as Part of STAF 2023, Leicester, UK, July 19–20, 2023, Proceedings
Editors	Maribel Fernández, Christopher M. Poskitt
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	102-122
Number of pages	21
ISBN (Electronic)	9783031367090
ISBN (Print)	9783031367083
DOIs	https://doi.org/10.1007/978-3-031-36709-0_6
Publication status	Published - 2023
Event	16th International Conference on Graph Transformation, ICGT 2023 - Leicester, United Kingdom Duration: 19 Jul 2023 → 20 Jul 2023

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	13961 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	16th International Conference on Graph Transformation, ICGT 2023
Country/Territory	United Kingdom
City	Leicester
Period	19/07/23 → 20/07/23

Bibliographical note

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

Funding

We thank Helle Hvid Hansen for discussions and valuable suggestions. The authors received funding from the Netherlands Organization for Scientific Research (NWO) under the Innovational Research Incentives Scheme Vidi (project. No. VI.Vidi.192.004).

Keywords

Fuzzy set
Graph rewriting
Presheaf
Quasitopos

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10.1007/978-3-031-36709-0_6

Fuzzy Presheaves are QuasitoposesFinal published version, 467 KBLicence: Article 25fa Dutch Copyright Act

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Rosset, A., Overbeek, R., & Endrullis, J. (2023). Fuzzy Presheaves are Quasitoposes. In M. Fernández, & C. M. Poskitt (Eds.), Graph Transformation: 16th International Conference, ICGT 2023, Held as Part of STAF 2023, Leicester, UK, July 19–20, 2023, Proceedings (pp. 102-122). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13961 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-36709-0_6

Rosset, Aloïs ; Overbeek, Roy ; Endrullis, Jörg. / Fuzzy Presheaves are Quasitoposes. Graph Transformation: 16th International Conference, ICGT 2023, Held as Part of STAF 2023, Leicester, UK, July 19–20, 2023, Proceedings. editor / Maribel Fernández ; Christopher M. Poskitt. Springer Science and Business Media Deutschland GmbH, 2023. pp. 102-122 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Rosset, A, Overbeek, R & Endrullis, J 2023, Fuzzy Presheaves are Quasitoposes. in M Fernández & CM Poskitt (eds), Graph Transformation: 16th International Conference, ICGT 2023, Held as Part of STAF 2023, Leicester, UK, July 19–20, 2023, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 13961 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 102-122, 16th International Conference on Graph Transformation, ICGT 2023, Leicester, United Kingdom, 19/07/23. https://doi.org/10.1007/978-3-031-36709-0_6

Fuzzy Presheaves are Quasitoposes. / Rosset, Aloïs; Overbeek, Roy; Endrullis, Jörg.
Graph Transformation: 16th International Conference, ICGT 2023, Held as Part of STAF 2023, Leicester, UK, July 19–20, 2023, Proceedings. ed. / Maribel Fernández; Christopher M. Poskitt. Springer Science and Business Media Deutschland GmbH, 2023. p. 102-122 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13961 LNCS).

Research output: Chapter in Book / Report / Conference proceeding › Conference contribution › Academic › peer-review

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Rosset A, Overbeek R, Endrullis J. Fuzzy Presheaves are Quasitoposes. In Fernández M, Poskitt CM, editors, Graph Transformation: 16th International Conference, ICGT 2023, Held as Part of STAF 2023, Leicester, UK, July 19–20, 2023, Proceedings. Springer Science and Business Media Deutschland GmbH. 2023. p. 102-122. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). Epub 2023 Jul 12. doi: 10.1007/978-3-031-36709-0_6

Fuzzy Presheaves are Quasitoposes

Abstract

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Bibliographical note

Funding

Keywords

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