[2205.07664v3] Promonads and String Diagrams for Effectful Categories
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Mathematics > Category Theory

arXiv:2205.07664v3 (math)
[Submitted on 16 May 2022 (v1), revised 31 Jul 2023 (this version, v3), latest version 1 May 2024 (v4)]

Title:Promonads and String Diagrams for Effectful Categories

Authors:Mario Román (Tallinn University of Technology)
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Abstract:Premonoidal and Freyd categories are both generalized by non-cartesian Freyd categories: effectful categories. We construct string diagrams for effectful categories in terms of the string diagrams for a monoidal category with a freely added object. We show that effectful categories are pseudomonoids in a monoidal bicategory of promonads with a suitable tensor product.
Comments: In Proceedings ACT 2022, arXiv:2307.15519
Subjects: Category Theory (math.CT); Logic in Computer Science (cs.LO)
Cite as: arXiv:2205.07664 [math.CT]
  (or arXiv:2205.07664v3 [math.CT] for this version)
  https://doi.org/10.48550/arXiv.2205.07664
Journal reference: EPTCS 380, 2023, pp. 344-361
Related DOI: https://doi.org/10.4204/EPTCS.380.20

Submission history

From: EPTCS [view email] [via EPTCS proxy]
[v1] Mon, 16 May 2022 13:27:52 UTC (2,820 KB)
[v2] Tue, 30 Aug 2022 13:47:15 UTC (2,805 KB)
[v3] Mon, 31 Jul 2023 10:41:09 UTC (1,483 KB)
[v4] Wed, 1 May 2024 19:06:35 UTC (5,534 KB)
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