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GReTA seminar #11: Rewriting Modulo Symmetric Monoidal Structure (by P. Sobociński)
*Please note:* as the seminar will be live-streamed to YouTube, we kindly ask participants to join the meeting ideally already during the 15min prior to the start of the talk at 15:00 (albeit the link will remain active throughout the duration of the event). After the talk, there will be a possibility to interact with the speaker and other participants during a 30min discussion session (not streamed to YouTube) starting from 16:00.


Abstract:

String diagrams are an elegant, convenient and powerful syntax for arrows of symmetric monoidal categories. In recent years, they have been used as compositional descriptions of computational systems from various fields, including quantum foundations, linear algebra, control theory, automata theory, concurrency theory, and even linguistics. All of these applications rely on diagrammatic reasoning, which is to string diagrams as equational reasoning is to ordinary terms.

If we are to take string diagrams out of research papers and into practical applications, we need understand how to implement diagrammatic reasoning. This is the focus of my talk.

There is a tight correspondence between symmetric monoidal categories where every object has a coherent special Frobenius algebra structure and categories of cospans of hypergraphs. This correspondence, therefore, takes us from a topological understanding of string diagrams to a combinatorial data-structure-like description. Moreover, diagrammatic reasoning translates via this correspondence exactly to DPO rewriting with interfaces.

The obvious follow-up question is: how much of this correspondence survives if we drop the assumption about Frobenius structure? Can we use this correspondence to implement diagrammatic reasoning on vanilla symmetric monoidal categories? The answer is yes, [...] (full abstract: https://www.irif.fr/~greta/talk/apr23th2021-sobocinski/)

Apr 23, 2021 02:45 PM in Paris

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