A Tangent Category Perspective on Connections in Algebraic Geometry
There is an abstract notion of connection in any tangent category. In this paper, we show that
when applied to the tangent category of affine schemes, this recreates the classical notion of …
when applied to the tangent category of affine schemes, this recreates the classical notion of …
Differential equations in a tangent category i: Complete vector fields, flows, and exponentials
This paper describes how to define and work with differential equations in the abstract
setting of tangent categories. The key notion is that of a curve object which is, for differential …
setting of tangent categories. The key notion is that of a curve object which is, for differential …
The Rosick\'y Tangent Categories of Algebras over an Operad
Tangent categories provide a categorical axiomatization of the tangent bundle. There are
many interesting examples and applications of tangent categories in a variety of areas such …
many interesting examples and applications of tangent categories in a variety of areas such …
On the geometric notion of connection and its expression in tangent categories
RBB Lucyshyn-Wright - arxiv preprint arxiv:1705.10857, 2017 - arxiv.org
Tangent categories provide an axiomatic approach to key structural aspects of differential
geometry that exist not only in the classical category of smooth manifolds but also in …
geometry that exist not only in the classical category of smooth manifolds but also in …
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 …
[PDF][PDF] Tangent∞-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 …
[PDF][PDF] HIGHER
S Ikonicoff, M Lanfranchi, JSP Lemay - 2024 - higher-structures.math.cas.cz
Tangent categories provide a categorical axiomatization of the tangent bundle. There are
many interesting examples and applications of tangent categories in a variety of areas such …
many interesting examples and applications of tangent categories in a variety of areas such …
[PDF][PDF] a review of Differential equations in a tangent category. I: Complete vector fields, flows, and exponentials by Cockett, JRB; Cruttwell, GSH; Lemay, J.-SP
西村泰一， ニシムラヒロカズ - zbMATH Open, 2022 - tsukuba.repo.nii.ac.jp
Cockett, JRB ; Cruttwell, GSH ; Lemay, J.-SP Differential equations in a tangent category. I:
Complete vector field Page 1 Cockett, JRB; Cruttwell, GSH; Lemay, J.-SP Differential equations …
Complete vector field Page 1 Cockett, JRB; Cruttwell, GSH; Lemay, J.-SP Differential equations …
[PDF][PDF] a review of Differential equations in a tangent category I: Complete vector fields, flows, and exponentials by Cockett, JRB (3-CALG-C); Cruttwell, GSH (3-MTAU); …
西村泰一， ニシムラヒロカズ - Mathematical Reviews …, 2020 - tsukuba.repo.nii.ac.jp
Appl. Categ. Structures 29 (2021), no. 5, 773–825. While many ideas from differential geometry
have been generalized to tangen Page 1 Previous Up Next Citations From References: 0 From …
have been generalized to tangen Page 1 Previous Up Next Citations From References: 0 From …
[PDF][PDF] Integration of 1-forms and connections
A Kock - arxiv preprint arxiv:1902.11003, 2019 - arxiv.org
arxiv:1902.11003v1 [math.DG] 28 Feb 2019 Integration of 1-forms and connections Page 1
arxiv:1902.11003v1 [math.DG] 28 Feb 2019 Integration of 1-forms and connections Anders …
arxiv:1902.11003v1 [math.DG] 28 Feb 2019 Integration of 1-forms and connections Anders …