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On the category of manifolds over algebras. (Russian) Zbl 0856.18009

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.

MSC:

18F15 Abstract manifolds and fiber bundles (category-theoretic aspects)
58A20 Jets in global analysis
58A05 Differentiable manifolds, foundations
18A23 Natural morphisms, dinatural morphisms
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