The Smash Product of Monoidal Theories
The tensor product of props was defined by Hackney and Robertson as an extension of the Boardman-Vogt product of operads to more general monoidal theories. Theories that factor as tensor products include the theory of commutative monoids and the theory of bialgebras. We give a topological interpreta...
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| Published in: | Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science pp. 1 - 13 |
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| Main Author: | |
| Format: | Conference Proceeding |
| Language: | English |
| Published: |
IEEE
29.06.2021
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| Subjects: | |
| Online Access: | Get full text |
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| Summary: | The tensor product of props was defined by Hackney and Robertson as an extension of the Boardman-Vogt product of operads to more general monoidal theories. Theories that factor as tensor products include the theory of commutative monoids and the theory of bialgebras. We give a topological interpretation (and vast generalisation) of this construction as a low-dimensional projection of a "smash product of pointed directed spaces". Here directed spaces are embodied by combinatorial structures called diagrammatic sets, while Gray products replace cartesian products. The correspondence is mediated by a web of adjunctions relating diagrammatic sets, pros, probs, props, and Gray-categories. The smash product applies to presentations of higher-dimensional theories and systematically produces higher-dimensional coherence data. |
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| DOI: | 10.1109/LICS52264.2021.9470575 |