Symmetric monoidal closure without a trace
Date(s) : 24/09/2026 iCal
11h00 - 12h30
In order to obtain semantics of programming languages with quantitative effects (such as probabilistic or quantum primitives), one common approach is to take a model of classical programming (eg games or relational models) and combine it with a category E expressing the desired quantitative effect. However such constructions usually require E to be symmetric monoidal closed, whereas some desired categories of quantitative effects desperately lack monoidal closure. So in this work we ask: how can we turn a symmetric monoidal category into a symmetric monoidal *closed* category? One recipe of particular interest is Joyal, Verity and Street’s « Int construction » that turns a traced monoidal category into a compact closed category. But what if there is no trace ?
In this talk, I will present a construction that turns any symmetric monoidal category into a *-autonomous category. The idea is to capture abstractly a phenomenon occurring in Paquet and Winskel’s game semantics for continuous probabilistic programming: there, an Int-like construction can be performed without a trace, exploiting an acyclicity property ensured by the combinatorics of concurrent games. Here instead, we replicate this phenomenon via a biorthogonality construction.
This is joint work with Kostia Chardonnet and Simon Forest.
Emplacement
I2M Luminy - TPR2, Salle de Séminaire 304-306 (3ème étage)
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