Taylor expansion as a monad in models of dill
Differential Linear Logic (DiLL) adds to Linear Logic (LL) a symmetrization of three out of the
four exponential rules, which allows the expression of a natural notion of differentiation. In …
four exponential rules, which allows the expression of a natural notion of differentiation. In …
Cartesian differential comonads and new models of cartesian differential categories
S Ikonicoff, JSP Lemay - arXiv preprint arXiv:2108.04304, 2021 - arxiv.org
Cartesian differential categories come equipped with a differential combinator that
formalizes the derivative from multi-variable differential calculus, and also provide the …
formalizes the derivative from multi-variable differential calculus, and also provide the …
On generalized metric spaces for the simply typed lambda-calculus
P Pistone - 2021 36th Annual ACM/IEEE Symposium on Logic …, 2021 - ieeexplore.ieee.org
Generalized metrics, arising from Lawvere's view of metric spaces as enriched categories,
have been widely applied in denotational semantics as a way to measure to which extent …
have been widely applied in denotational semantics as a way to measure to which extent …
Monoidal bicategories, differential linear logic, and analytic functors
We develop further the theory of monoidal bicategories by introducing and studying bicate-
gorical counterparts of the notions of a linear explonential comonad, as considered in the …
gorical counterparts of the notions of a linear explonential comonad, as considered in the …
Koszul duality, minimal model and L∞-structure for differential algebras with weight
J Chen, L Guo, K Wang, G Zhou - Advances in Mathematics, 2024 - Elsevier
A differential algebra with weight is an abstraction of both the derivation (weight zero) and
the forward and backward difference operators (weight±1). In 2010 Loday established the …
the forward and backward difference operators (weight±1). In 2010 Loday established the …
Graded differential categories and graded differential linear logic
JSP Lemay, JB Vienney - Electronic Notes in Theoretical …, 2023 - entics.episciences.org
Abstract In Linear Logic (LL), the exponential modality! brings forth a distinction between
non-linear proofs and linear proofs, where linear means using an argument exactly once …
non-linear proofs and linear proofs, where linear means using an argument exactly once …
Free commutative monoids in homotopy type theory
V Choudhury, M Fiore - Electronic Notes in Theoretical …, 2023 - entics.episciences.org
We develop a constructive theory of finite multisets in Homotopy Type Theory, defining them
as free commutative monoids. After recalling basic structural properties of the free …
as free commutative monoids. After recalling basic structural properties of the free …
Tangent categories from the coalgebras of differential categories
Following the pattern from linear logic, the coKleisli category of a differential category is a
Cartesian differential category. What then is the coEilenberg-Moore category of a differential …
Cartesian differential category. What then is the coEilenberg-Moore category of a differential …
Strategies as resource terms, and their categorical semantics
L Blondeau-Patissier, P Clairambault… - arXiv preprint arXiv …, 2023 - arxiv.org
As shown by Tsukada and Ong, normal (extensional) simply-typed resource terms
correspond to plays in Hyland-Ong games, quotiented by Melli\es' homotopy equivalence …
correspond to plays in Hyland-Ong games, quotiented by Melli\es' homotopy equivalence …
Coherent differentiation
T Ehrhard - Mathematical Structures in Computer Science, 2023 - cambridge.org
The categorical models of differential linear logic (LL) are additive categories and those of
the differential lambda-calculus are left-additive categories because of the Leibniz rule …
the differential lambda-calculus are left-additive categories because of the Leibniz rule …