[2103.00938v3] Differential 2-rigs
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Mathematics > Category Theory

arXiv:2103.00938v3 (math)
[Submitted on 1 Mar 2021 (v1), last revised 31 Jul 2023 (this version, v3)]

Title:Differential 2-rigs

Authors:Fosco Loregian (Tallinn University of Technology), Todd Trimble (Western Connecticut State University)
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Abstract:We study the notion of a "differential 2-rig", a category R with coproducts and a monoidal structure distributing over them, also equipped with an endofunctor D : R -> R that satisfies a categorified analogue of the Leibniz rule. This is intended as a tool to unify various applications of such categories to computer science, algebraic topology, and enumerative combinatorics. The theory of differential 2-rigs has a geometric flavour but boils down to a specialization of the theory of tensorial strengths on endofunctors; this builds a surprising connection between apparently disconnected fields. We build "free 2-rigs" on a signature, and we prove various initiality results: for example, a certain category of colored species is the free differential 2-rig on a single generator.
Comments: In Proceedings ACT 2022, arXiv:2307.15519
Subjects: Category Theory (math.CT)
Cite as: arXiv:2103.00938 [math.CT]
  (or arXiv:2103.00938v3 [math.CT] for this version)
  https://doi.org/10.48550/arXiv.2103.00938
Journal reference: EPTCS 380, 2023, pp. 159-182
Related DOI: https://doi.org/10.4204/EPTCS.380.10

Submission history

From: EPTCS [view email] [via EPTCS proxy]
[v1] Mon, 1 Mar 2021 12:02:02 UTC (41 KB)
[v2] Fri, 11 Mar 2022 11:35:04 UTC (80 KB)
[v3] Mon, 31 Jul 2023 10:30:20 UTC (37 KB)
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