Smooth coalgebras

Details Smooth coalgebras Smooth coalgebras

1997-12-23

arxiv.org/abs/physics/9712045v1

Physics

Mathematical Physics

LaTeX, 60 pages

Scientific paper

A complete mathematical framework for coalgebraic formulation of supergeometry and its infinite-dimensional extension is proposed. Within this approach a supermanifold is defined as a graded coalgebra endowed with a smooth structure. The category of such coalgebras is constructed and analysed. It is shown that it contains as its full subcategories both the category of smooth Fr\'{e}chet manifolds and the category of finite-dimensional Berezin-Leites-Kostant supermanifolds.

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