ERATO Project Colloquium by Masahiro Hamano, prof. Miin Wu School of Computing, Taiwan, will be held on June 21st
Theme of the lecture:
A Linear Exponential Comonad in s-finite Transition Kernels and Probabilistic Coherent Spaces
Professor of Miin Wu School of Computing, Project Professor of National Cheng Kung University, Taiwan
16:30- / Tuesday, June 21st, 2022
If you would like to attend, please register through the following Google form:
A zoom link will be sent to you via e-mail. (using BCC).
This talk presents a novel construction of linear exponential comonad arising properly in the continuous measure-theory. Our construction in particular gives a discrete measure account of Danos-Ehrhard 's probabilistic coherent spaces.
The talk starts with constructing a linear exponential comonad over a symmetric monodical category of transition kernels, relaxing Markov kernels of Panangaden's stochastic relations into Staton's s-finite kernels.
Our model supports an orthogonality in terms of an integral between measures and measurable functions, which can be seen as a continuous extension of Girard-Danos-Ehrhard' s linear duality for probabilistic coherent spaces.
The orthogonality is formulated by Hyland-Schalk double glueing construction, into which our measure theoretic monoidal comonad structure is accommodated.
As an application to countable measurable spaces, a dagger compact closed category is obtained, whose double glueing gives rise to the familiar category of probabilistic coherent spaces.
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