Corpus ID: 119133052

Affine geometric spaces in tangent categories

@article{Blute2018AffineGS,
  title={Affine geometric spaces in tangent categories},
  author={R. Blute and G. Cruttwell and R. B. Lucyshyn-Wright},
  journal={arXiv: Category Theory},
  year={2018}
}
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 category of smooth manifolds. In classical geometry, having an affine structure on a manifold is equivalent to having a flat torsion-free connection on its tangent bundle. This equivalence allows us to define a category of affine objects associated to a tangent category and we show that the resulting category is also… Expand

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