# Double Glueing over Free Exponential: with Measure Theoretic Applications

@article{Hamano2021DoubleGO, title={Double Glueing over Free Exponential: with Measure Theoretic Applications}, author={Masahiro Hamano}, journal={ArXiv}, year={2021}, volume={abs/2107.07726} }

This paper provides a compact method to lift the free exponential construction of Melliès-Tabareau-Tasson over the Hyland-Schalk double glueing for orthogonality categories. A condition ”reciprocity of orthogonality” is presented simply enough to lift the free exponential over the double glueing in terms of the orthogonality. Our general method applies to the monoidal category TsK of the s-finite transition kernels with countable biproducts. We show (i) TsK has the free exponential, which is…

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