Connections in Tangent Categories

zbMath1374.18016arXiv1610.08774MaRDI QIDQ5364129

G. S. H. Cruttwell, J. Robin B. Cockett

Publication date: 4 October 2017

Full work available at URL: https://arxiv.org/abs/1610.08774

zbMATH Keywords

curvature tensordynamical systemFinsler connectionhorizontal connectionabstract curvatureabstract torsionbundle morphisms in TCcanonical(affine) verical connectionconnection on a differential bundlecovariant derivative of a vertical connectioncurvature of a verical connectiondifferential bundle in TCflat vertical connectionparallel transport.tangent categories (TC)torsion-free vertical connectiontotal curvature objectvertical connections

Mathematics Subject Classification ID

Linear and affine connections (53B05) Other connections (53B15) Categorical structures (18D99) Synthetic differential geometry (51K10)

Related Items (8)

Unnamed Item ⋮ Differential equations in a tangent category. I: Complete vector fields, flows, and exponentials ⋮ Game comparison through play ⋮ On the geometric notion of connection and its expression in tangent categories ⋮ Exponential functions in Cartesian differential categories ⋮ Vector bundles and differential bundles in the category of smooth manifolds ⋮ Affine geometric spaces in tangent categories ⋮ Unnamed Item

Cites Work

• Functional distribution monads in functional-analytic contexts
• Differential structure, tangent structure, and SDG
• Ordinary differential equations and their exponentials
• On the Geometry of the Tangent Bundle.
• Connexions and Prolongations
• Connections, Sprays and Finsler Structures
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Connections in Tangent Categories