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arXiv · 1406.6717

Homological Algebra for Diffeological Vector Spaces

Enxin Wu
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Abstract

Diffeological spaces are natural generalizations of smooth manifolds, introduced by J.M.~Souriau and his mathematical group in the 1980's. Diffeological vector spaces (especially fine diffeological vector spaces) were first used by P. Iglesias-Zemmour to model some infinite dimensional spaces in~\cite{I1,I2}. K.~Costello and O.~Gwilliam developed homological algebra for differentiable diffeological vector spaces in Appendix A of their book~\cite{CG}. In this paper, we present homological algebra of general diffeological vector spaces via the projective objects with respect to all linear subductions, together with some applications in analysis.

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Enxin Wu. 2014-06-25. Homological Algebra for Diffeological Vector Spaces. https://arxiv.org/abs/1406.6717

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