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Dec 19, 2020 at 1:38 comment added Robbie Lyman It's not hard to show that morphisms may be composed under this definition. The definition Satake is referring to in his footnote is different: in that definition a smooth map $f\colon M \to N$ is a collection of mappings from an atlas of charts for $M$ to charts for $N$ satisfying a compatibility condition
Mar 9, 2017 at 8:52 comment added Patrick I-Z This definition makes smooth maps between orbifolds not composable, as underlined by Satake in his original paper in 1957, see the counter-example we gave below.
Dec 14, 2013 at 9:52 vote accept Bruno Martelli
Dec 14, 2013 at 9:47 comment added Bruno Martelli thank you for the reference! I accept this answer because the reference is closer to the definition I know, but I thank everybody for providing more "enlightening" definitions :-)
Dec 13, 2013 at 20:58 history edited Claudio Gorodski CC BY-SA 3.0
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Dec 13, 2013 at 17:36 history answered Claudio Gorodski CC BY-SA 3.0