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Metric Algebra

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If you have a question about this talk, please contact Tamara von Glehn.

I shall present work in progress that extends the algebraic-theory/monad/equational-logic correspondence of universal algebra to the metric context. As a matter of background, I will recall the first part of this fundamental correspondence in the setting of a recent enriched theory/monad correspondence developed by Bourke and Garner [1]. The core of the talk will then be to analyze the abstract theory further and thereby define metric algebraic theories and synthesise a corresponding metric equational logic. The resulting deductive system subsumes the equational logic for quantitative algebraic reasoning introduced by Mardare, Panangaden, and Plotkin [2].

References

[1] J Bourke and R Garner. Monads and theories. arXiv, 2018.

[2] R Mardare, P Panangaden, and G Plotkin. Quantitative Algebraic Reasoning. LICS , 2016.

This talk is part of the Category Theory Seminar series.

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