Homological Algebra for Diffeological Vector Spaces
K-Theory and Homology
2014-06-27 v1
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.
Keywords
Cite
@article{arxiv.1406.6717,
title = {Homological Algebra for Diffeological Vector Spaces},
author = {Enxin Wu},
journal= {arXiv preprint arXiv:1406.6717},
year = {2014}
}