Convolution Products on Double Categories and Categorification of Rule Algebras - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2023

Convolution Products on Double Categories and Categorification of Rule Algebras

Résumé

Motivated by compositional categorical rewriting theory, we introduce a convolution product over presheaves of double categories which generalizes the usual Day tensor product of presheaves of monoidal categories. One interesting aspect of the construction is that this convolution product is in general only oplax associative. For that reason, we identify several classes of double categories for which the convolution product is not just oplax associative, but fully associative. This includes in particular framed bicategories on the one hand, and double categories of compositional rewriting theories on the other. For the latter, we establish a formula which justifies the view that the convolution product categorifies the rule algebra product.
Fichier principal
Vignette du fichier
LIPIcs.FSCD.2023.17.pdf (2.27 Mo) Télécharger le fichier
Origine : Fichiers éditeurs autorisés sur une archive ouverte
Licence : CC BY - Paternité

Dates et versions

hal-04222049 , version 1 (24-11-2023)

Identifiants

Citer

Nicolas Behr, Paul-André Melliès, Noam Zeilberger. Convolution Products on Double Categories and Categorification of Rule Algebras. FSCD 2023 - 8th International Conference on Formal Structures for Computation and Deduction, Jul 2023, Rome, Italy. pp.17:1-17:20, ⟨10.4230/LIPIcs.FSCD.2023.17⟩. ⟨hal-04222049⟩
48 Consultations
11 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More