Online algebra seminar - June 10th, 1pm |
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We will continue online on Thursday, June 10th, at 13.00 CEST on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:
Noam Zeilberger
Skew monoidal categories and the proof-theoretic anatomy of associativity (and unitality)
Abstract: Based on joint work with Tarmo Uustalu and Niccolò Veltri. The talk will survey a recent line of work, which takes a proof-theoretic approach to solving the coherence problem(s) for skew monoidal categories and related structures. I will begin by discussing the so-called Tamari order on fully-bracketed words induced by a semi-associative law (AB)C <= A(BC), and explain how a simple sequent calculus may account for some of its fascinating properties, such as the fact that the set of fully-bracketed words on n+1 letters forms a lattice Y_n under this order, as well as a remarkable formula counting the number of intervals in Y_n. Then I will recall the definition of skew monoidal categories, and explain how a more refined sequent calculus may be used to solve two related coherence problems: deciding equality of maps and enumerating homsets in free skew monoidal categories. Closely related to recent work by Bourke and Lack, this sequent calculus may be considered as a canonical construction of the free left representable skew multicategory over a set of atoms. Finally, I will briefly discuss variations of the sequent calculus capturing "partially skew" monoidal categories with different normality conditions. References: [1] https://arxiv.org/abs/1803.10080 [2] https://arxiv.org/abs/2003.05213 [3] https://arxiv.org/abs/2101.10487
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Last Updated on Wednesday, 09 June 2021 07:45 |