[Submitted on 8 Aug 2025 (v1), last revised 24 Jun 2026 (this version, v3)]

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Abstract:It is well-known that pseudofunctors from bicategories of spans are equivalent to Beck-Chevalley bifibrations, and therefore capture the relationships underlying the adjunctions suitable as semantics for existential quantification. This was further expanded upon by Dawson, Paré and Pronk in the context of double categories. By viewing hyperdoctrines from a double-categorical lens, this paper shows that we can also characterise the Frobënius property: (generalised) regular hyperdoctrines correspond to certain lax symmetric monoidal pseudo double functors from spans to quintets whose monoidal laxators provide companion commuter cells (in the sense of Paré). This facilitates the study of the compositionality of regular hyperdoctrines and hints at a new notion of regular double hyperdoctrine. As an application, we discuss how we can recover a form of graphical regular logic suitable for modelling specifications of systems (e.g., port-plugging systems) that compose operadically.

Submission history

From: José Siqueira [view email]
[v1] Fri, 8 Aug 2025 18:34:36 UTC (63 KB)
[v2] Wed, 24 Sep 2025 20:56:08 UTC (67 KB)
[v3] Wed, 24 Jun 2026 15:57:13 UTC (65 KB)

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