Cartesian Differential Kleisli Categories
JSP Lemay - Electronic Notes in Theoretical Informatics and …, 2023 - entics.episciences.org
Cartesian differential categories come equipped with a differential combinator which
axiomatizes the fundamental properties of the total derivative from differential calculus. The …
axiomatizes the fundamental properties of the total derivative from differential calculus. The …
Exponential functions in cartesian differential categories
JSP Lemay - Applied Categorical Structures, 2021 - Springer
In this paper, we introduce differential exponential maps in Cartesian differential categories,
which generalizes the exponential function e^ x ex from classical differential calculus. A …
which generalizes the exponential function e^ x ex from classical differential calculus. A …
Cartesian differential categories as skew enriched categories
We exhibit the cartesian differential categories of Blute, Cockett and Seely as a particular
kind of enriched category. The base for the enrichment is the category of commutative …
kind of enriched category. The base for the enrichment is the category of commutative …
A Tangent Category Alternative to the Fa\a di Bruno Construction
JS Lemay - arXiv preprint arXiv:1805.01774, 2018 - arxiv.org
The Fa\a di Bruno construction, introduced by Cockett and Seely, constructs a comonad
$\mathsf {Fa {\grave {a}}} $ whose coalgebras are precisely Cartesian differential categories …
$\mathsf {Fa {\grave {a}}} $ whose coalgebras are precisely Cartesian differential categories …
A simplicial foundation for differential and sector forms in tangent categories
GSH Cruttwell, RBB Lucyshyn-Wright - Journal of Homotopy and Related …, 2018 - Springer
Tangent categories provide an axiomatic framework for understanding various tangent
bundles and differential operations that occur in differential geometry, algebraic geometry …
bundles and differential operations that occur in differential geometry, algebraic geometry …
Affine geometric spaces in tangent categories
RF Blute, GSH Cruttwell… - arXiv preprint arXiv …, 2018 - arxiv.org
We continue the program of structural differential geometry that begins with the notion of a
tangent category, an axiomatization of structural aspects of the tangent functor on the …
tangent category, an axiomatization of structural aspects of the tangent functor on the …
Tangent infinity-categories and goodwillie calculus
We make precise the analogy between Goodwillie's calculus of functors in homotopy theory
and the differential calculus of smooth manifolds by introducing a higher-categorical …
and the differential calculus of smooth manifolds by introducing a higher-categorical …
Cofibrantly generated model structures for functor calculus
L Bandklayder, JE Bergner, R Griffiths… - arXiv preprint arXiv …, 2023 - arxiv.org
Model structures for many different kinds of functor calculus can be obtained by applying a
theorem of Bousfield to a suitable category of functors. In this paper, we give a general …
theorem of Bousfield to a suitable category of functors. In this paper, we give a general …
The functorial semantics of Lie theory
B MacAdam - arXiv preprint arXiv:2301.00305, 2022 - arxiv.org
Ehresmann's introduction of differentiable groupoids in the 1950s may be seen as a starting
point for two diverging lines of research, many-object Lie theory (the study of Lie algebroids …
point for two diverging lines of research, many-object Lie theory (the study of Lie algebroids …