The existence of models of pseudo-Riemannian spaces in synthetic differential geometry (Q2713878)

Let \(\mathcal E\) be a category of models of synthetic differential geometry and let \(Mf\) be the category of smooth manifolds and smooth maps. Then there exists a complete exact functor \(i: Mf \to \mathcal E\). NEWLINENEWLINENEWLINEThe author considers a pseudo-Riemannian manifold which is an object in \(Mf\) and reformulates the axioms of pseudo-Riemannian manifolds in the language of diagrams. Under this approach, \(i(M)\), with \(M\in Mf\), is an object in the category \(\mathcal E\) which satisfies the axioms of pseudo-Riemannian spaces in the synthetic differential geometry.NEWLINENEWLINEFor the entire collection see [Zbl 0935.00013].