Abstract
We formalise strict 2-catoids, 2-categories, 2-Kleene algebras
and 2-quantales, as well as their omega-variants. Due to
strictness, the cells of these higher categories have globular
shape. We use a single-set approach, generalised to catoids and
based on type classes. The higher Kleene algebras and quantales
introduced extend features of modal and concurrent Kleene algebras
and quantales. They arise for instance as powerset extensions of
higher catoids, and have been used in algebraic confluence proofs in
higher-dimensional rewriting. Details are described in two companion
articles.
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Related publications
- Calk, C., Goubault, E., Malbos, P., & Struth, G. (2022). Algebraic coherent confluence and higher globular Kleene algebras. Logical Methods in Computer Science, Volume 18, Issue 4. https://doi.org/10.46298/lmcs-18(4:9)2022
- Calk, C., Malbos, P., Pous, D., & Struth, G. (2023). Higher Catoids, Higher Quantales and their Correspondences (Version 2). arXiv. https://doi.org/10.48550/ARXIV.2307.09253