Bonjour! Demain, à 10h30 en B107, Jad Koleilat nous parlera sur le sujet suivant. --- Cartesian Differential Categories are a categorical axiomatisation of differentiation between vector spaces. A CDC is a cartesian category equipped with a differential operator, associating to each morphism f : A -> B a morphism Df : A x A -> B. The category of real finite dimentional vector spaces and smooth function is an example of CDC. Historically, they were discovered wile studying categorical models of a certain logic called Differential Linear Logic (DiLL). Since 2021, we know that there exists a strong duality between CDC and models of DiLL : the coKleisli of every model of DiLL is a CDC and every CDC embeds fully and faithfully into the coKleisli of a model of DiLL. This duality can appear somewhat surprising as it is not often that such logical/mathematical duality exists especially in the context of non-discrete structures. In this talk, I will explain what are CDC, what are models of DiLL, the duality between them and try to convey the intuitions I have on those structures. --- Il est possible que la réunion soit plus court que d'habitude. Bien cordialement, Morgan Rogers
Bonjour, Je suis désolé, je pourrai peut-être me connecter en visio (avec départ impérativement à 11h30), mais ce n'est pas certain. À bientôt, Aurélien. Le 12/02/2026 à 15:40, Groupe de travail catégories a écrit :
Bonjour!
Demain, à 10h30 en B107, Jad Koleilat nous parlera sur le sujet suivant. --- Cartesian Differential Categories are a categorical axiomatisation of differentiation between vector spaces. A CDC is a cartesian category equipped with a differential operator, associating to each morphism f : A -> B a morphism Df : A x A -> B. The category of real finite dimentional vector spaces and smooth function is an example of CDC.
Historically, they were discovered wile studying categorical models of a certain logic called Differential Linear Logic (DiLL). Since 2021, we know that there exists a strong duality between CDC and models of DiLL : the coKleisli of every model of DiLL is a CDC and every CDC embeds fully and faithfully into the coKleisli of a model of DiLL. This duality can appear somewhat surprising as it is not often that such logical/mathematical duality exists especially in the context of non-discrete structures.
In this talk, I will explain what are CDC, what are models of DiLL, the duality between them and try to convey the intuitions I have on those structures. --- Il est possible que la réunion soit plus court que d'habitude.
Bien cordialement, Morgan Rogers _______________________________________________ Categories mailing list Categories@lipn.univ-paris13.fr https://lipn.univ-paris13.fr/listes-lipn/listinfo/categories
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