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The smash product of monoidal theories

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If you have a question about this talk, please contact Miriam Backens.

The smash product of pointed spaces is a classical construction of topology. The tensor product of props, which extends both the Boardman-Vogt product of symmetric operads and the tensor product of Lawvere theories to more general “monoidal theories”, is a piece of categorical universal algebra. In this talk, we will see that the two are facets of the same construction: a “smash product of pointed directed spaces”. Here, “directed spaces” are modelled by combinatorial structures called diagrammatic sets, developed as a homotopically sound foundation for diagrammatic rewriting in higher dimensions. Most interestingly, the smash product applies to presentations of higher-dimensional theories and systematically produces oriented equations and higher-dimensional coherence data. This introduces a new synthetic, compositional method in rewriting on higher structures. This talk is based on my preprint arXiv:2101.10361 with the same title.

This talk is part of the Theoretical computer science seminar series.

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