Mixed Linear-Cartesian Theories as Substitution Monoids

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• Sanjiv Ranchod (University of Cambridge)
• Monday 25 November 2024, 13:00-14:00
• FS07, Computer Laboratory.

If you have a question about this talk, please contact Dr Meven Lennon-Bertrand.

In [FPT], Fiore, Plotkin and Turi characterise first-order cartesian (that is, algebraic or Lawvere) theories as monoids for a particular substitution tensor. Similarly, in [K], Kelly characterises first-order linear theories (that is, operads) as monoids for a similarly defined substitution tensor. A mixed linear-cartesian theory is a first-order theory that combines and generalises these two cases. I will chat about the constructions of these cases and present work-in-progress on the construction of a tensor and monoid for the mixed theories.

[FPT] Fiore, M., Plotkin, G., and Turi, D. Abstract syntax and variable binding (extended abstract). In 14th Symposium on Logic in Computer Science. 1999.

[K] Kelly, G. M. On the operads of J.P. May. Reprints in Theory and Applications of Categories. 2005.

This talk is part of the SANDWICH Seminar (Computer Laboratory) series.

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• FS07, Computer Laboratory
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