Dear all,
On Tuesday June 21st, Masahiro Hamano (Miin Wu School of Computing, National Cheng Kung University) will give a talk, A Linear Exponential Comonad in s-finite Transition Kernels and Probabilistic Coherent Spaces, for our project colloquium during at 16:30. Further details can be found below.
If you would like to attend, please register through the following Google form: https://forms.gle/6PoGNEfJVHLYDAdKA We later send you a zoom link by an email (using BCC).
For the latest information about ERATO colloquium / seminar, please see the webpage https://docs.google.com/document/d/1Qrg4c8XDkbO3tmns6tQwxn5lGHOrBON5LtHXXTpX... .
Clovis Eberhart (ERATO MMSD Colloquium Organizer) Shin-ya Katsumata Email: eberhart@nii.ac.jp, s-katsumata@nii.ac.jp ------- Tuesday June 21st 16:30
Speaker: Masahiro Hamano (Miin Wu School of Computing, National Cheng Kung University)
Title: A Linear Exponential Comonad in s-finite Transition Kernels and Probabilistic Coherent Spaces
Abstract: 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.