On diffeological spaces as a fairly convenient model for generalized smooth spaces:
Alexander Hoffnung: Smooth spaces: convenient categories for differential geometry, talk slides (2009) [pdf]
Alexander Hoffnung: From Smooth Spaces to Smooth Categories, talk slides (2009) [pdf]
John Baez, Alexander Hoffnung: Convenient Categories of Smooth Spaces, Trans. Amer. Math. Soc. 363 11 (2011) 5789-5825 [doi:10.1090/S0002-9947-2011-05107-X, arXiv:0807.1704, blog]
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