@inproceedings{2e8947282d6d4a6b9d59c447dd1c9b81,
title = "Convolution Products on Double Categories and Categorification of Rule Algebras",
abstract = "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.",
keywords = "Categorical rewriting, convolution product, double categories, double pushout, framed bicategories, opfibrations, presheaf categories, rule algebra, sesqui-pushout",
author = "Nicolas Behr and Melli{\`e}s, \{Paul Andr{\'e}\} and Noam Zeilberger",
note = "Publisher Copyright: {\textcopyright} Nicolas Behr, Paul-Andr{\'e} Melli{\`e}s, and Noam Zeilberger.; 8th International Conference on Formal Structures for Computation and Deduction, FSCD 2023 ; Conference date: 03-07-2023 Through 06-07-2023",
year = "2023",
month = jun,
day = "1",
doi = "10.4230/LIPIcs.FSCD.2023.17",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Marco Gaboardi and \{van Raamsdonk\}, Femke",
booktitle = "8th International Conference on Formal Structures for Computation and Deduction, FSCD 2023",
}