[2307.16558] Canonical Gradings of Monads
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Computer Science > Logic in Computer Science

arXiv:2307.16558 (cs)
[Submitted on 31 Jul 2023]

Title:Canonical Gradings of Monads

Authors:Flavien Breuvart, Dylan McDermott, Tarmo Uustalu
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Abstract:We define a notion of grading of a monoid T in a monoidal category C, relative to a class of morphisms M (which provide a notion of M-subobject). We show that, under reasonable conditions (including that M forms a factorization system), there is a canonical grading of T. Our application is to graded monads and models of computational effects. We demonstrate our results by characterizing the canonical gradings of a number of monads, for which C is endofunctors with composition. We also show that we can obtain canonical grades for algebraic operations.
Comments: In Proceedings ACT 2022, arXiv:2307.15519
Subjects: Logic in Computer Science (cs.LO); Programming Languages (cs.PL); Category Theory (math.CT)
Cite as: arXiv:2307.16558 [cs.LO]
  (or arXiv:2307.16558v1 [cs.LO] for this version)
  https://doi.org/10.48550/arXiv.2307.16558
Journal reference: EPTCS 380, 2023, pp. 1-21
Related DOI: https://doi.org/10.4204/EPTCS.380.1

Submission history

From: EPTCS [view email] [via EPTCS proxy]
[v1] Mon, 31 Jul 2023 10:37:41 UTC (31 KB)
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