Shurygin, V. V. On the category of manifolds over algebras. (Russian) Zbl 0856.18009 Tr. Geom. Semin. 22, 107-122 (1994). For the category \({\mathcal A}\) of associative commutative finite-dimensional algebras over \(\mathbb{R}\) the author constructs a category \({\mathcal A}\)-Man of smooth manifolds modelled on modules over algebras of \({\mathcal A}\). Then submanifolds of manifolds of \({\mathcal A}\)-Man and jet bundles over manifolds of \({\mathcal A}\)-Man are studied. Reviewer: A.P.Shirokov (Kazan’) Cited in 2 Documents MSC: 18F15 Abstract manifolds and fiber bundles (category-theoretic aspects) 58A20 Jets in global analysis 58A05 Differentiable manifolds, foundations 18A23 Natural morphisms, dinatural morphisms Keywords:prolongation functor; natural functor equivalence; manifold over algebra; foliation; jet bundles PDFBibTeX XMLCite \textit{V. V. Shurygin}, Tr. Geom. Semin. 22, 107--122 (1994; Zbl 0856.18009) Full Text: EuDML