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== References == {{Reflist|refs= <ref name="Spiv65">{{Cite book |last=Spivak |first=Michael |author-link=Michael Spivak |title=Calculus on manifolds: a modern approach to classical theorems of advanced calculus |title-link=Calculus on Manifolds (book) |date=1965 |publisher=[[Benjamin Cummings]] |isbn=978-0-8053-9021-6 |series=Mathematics monograph series |location=Redwood city (Calif.)}}</ref> <ref name="Mun91">{{Cite book |last=Munkres |first=James R. |author-link=James Munkres |url=https://www.taylorfrancis.com/books/9780429962691 |title=Analysis on Manifolds |date=2018-02-19 |publisher=[[CRC Press]] |isbn=978-0-429-49414-7 |edition=1 |language=en |doi=10.1201/9780429494147}}</ref> <ref name="KobNom96">{{Cite book |last1=Kobayashi |first1=Shōshichi |author-link1=Shoshichi Kobayashi |title=Foundations of differential geometry. 1 |title-link=Foundations of Differential Geometry |last2=Nomizu |first2=Katsumi |author-link2=Katsumi Nomizu |date=1996 |publisher=[[Wiley (publisher)|Wiley]] |isbn=978-0-471-15733-5 |place=New York}}</ref> <ref name="Tu11">{{Cite book |last=Tu |first=Loring W. |author-link=Loring W. Tu |url=https://link.springer.com/book/10.1007/978-1-4419-7400-6 |title=An Introduction to Manifolds |series=Universitext |date=2011 | publisher=[[Springer Nature|Springer]] |language=en |doi=10.1007/978-1-4419-7400-6 |isbn=978-1-4419-7399-3 |issn=0172-5939}}</ref> <ref name="Lee13">{{Cite book |last=Lee |first=John M. |author-link=John M. Lee |url=https://link.springer.com/book/10.1007/978-1-4419-9982-5 |title=Introduction to Smooth Manifolds |series=Graduate Texts in Mathematics |date=2012 |volume=218 |publisher=[[Springer Nature|Springer]] |language=en |doi=10.1007/978-1-4419-9982-5 |isbn=978-1-4419-9981-8 |issn=0072-5285}}</ref> <ref name="Igl13">{{Cite book |last=Iglesias-Zemmour |first=Patrick |url=https://www.ams.org/surv/185 |title=Diffeology |date=2013-04-09 |publisher=[[American Mathematical Society]] |isbn=978-0-8218-9131-5 |series=[[Mathematical Surveys and Monographs]] |volume=185 |language=en |doi=10.1090/surv/185}}</ref> <ref name="Igl21">{{Citation |last=Iglesias-Zemmour |first=Patrick |title=An Introduction to Diffeology |date=2021 |work=New Spaces in Mathematics: Formal and Conceptual Reflections |volume=1 |pages=31–82 |editor-last=Catren |editor-first=Gabriel |url=https://math.huji.ac.il/~piz/documents/AITD.pdf |access-date=2025-03-17 |place=Cambridge |publisher=[[Cambridge University Press]] |doi=10.1017/9781108854429.003 |isbn=978-1-108-49063-4 |editor2-last=Anel |editor2-first=Mathieu}}</ref> <ref name="Igl22">{{Cite book |last=Iglesias-Zemmour |first=Patrick |url=https://mp.weixin.qq.com/s?__biz=MjM5NzE3Nzc4MQ==&mid=2664511235&idx=2&sn=a2b55b7fc0e88a3ae4142a8f53077055 |title=Diffeology |date=2022 |publisher=Beijing World Publishing Corporation |isbn=9787519296087 |language=en}}</ref> <ref name="Sour80">{{Citation |last=Souriau |first=J. M. |author-link=Jean-Marie Souriau |title=Groupes differentiels |date=1980 |work=Differential Geometrical Methods in Mathematical Physics |volume=836 |pages=91–128 |editor-last=García |editor-first=P. L. |url=http://link.springer.com/10.1007/BFb0089728 |access-date=2022-01-16 |series=Lecture Notes in Mathematics |place=Berlin, Heidelberg |publisher=Springer Berlin Heidelberg |doi=10.1007/bfb0089728 |isbn=978-3-540-10275-5 |editor2-last=Pérez-Rendón |editor2-first=A. |editor3-last=Souriau |editor3-first=J. M.}}</ref> <ref name="Sour84">{{Citation |last=Souriau |first=Jean-Marie |author-link=Jean-Marie Souriau |title=Groupes différentiels et physique mathématique |date=1984 |work=Group Theoretical Methods in Physics |volume=201 |pages=511–513 |editor-last=Denardo |editor-first=G. |url=http://link.springer.com/10.1007/BFb0016198 |access-date=2022-01-16 |series=Lecture Notes in Physics |place=Berlin/Heidelberg |publisher=Springer-Verlag |language=en |doi=10.1007/bfb0016198 |isbn=978-3-540-13335-3 |editor2-last=Ghirardi |editor2-first=G. |editor3-last=Weber |editor3-first=T.}}</ref> <ref name="Don84">{{Cite book |last=Donato |first=Paul |title=Revêtement et groupe fondamental des espaces différentiels homogènes |publisher=ScD thesis, [[Université de Provence]] |year=1984 |location=Marseille |language=fr |trans-title=Coverings and fundamental groups of homogeneous differential spaces}}</ref> <ref name="Igl85">{{Cite book |last=Iglesias |first=Patrick |url=https://math.huji.ac.il/~piz/documents/TheseEtatPI.pdf |title=Fibrés difféologiques et homotopie |publisher=ScD thesis, [[Université de Provence]] |year=1985 |location=Marseille |language=fr |trans-title=Diffeological fiber bundles and homotopy}}</ref> <ref name="Chen77">{{Cite journal |last=Chen |first=Kuo-Tsai |date=1977 |title=Iterated path integrals |url=https://www.ams.org/bull/1977-83-05/S0002-9904-1977-14320-6/ |journal=[[Bulletin of the American Mathematical Society]] |language=en |volume=83 |issue=5 |pages=831–879 |doi=10.1090/S0002-9904-1977-14320-6 |issn=0002-9904 |doi-access=free}}</ref> <ref name="BaezHof11">{{Cite journal |last1=Baez |first1=John |last2=Hoffnung |first2=Alexander |date=2011 |title=Convenient categories of smooth spaces |url=https://www.ams.org/tran/2011-363-11/S0002-9947-2011-05107-X/ |journal=[[Transactions of the American Mathematical Society]] |language=en |volume=363 |issue=11 |pages=5789–5825 |arxiv=0807.1704 |doi=10.1090/S0002-9947-2011-05107-X |issn=0002-9947 |doi-access=free}}</ref> <ref name="ChrSinWu14">{{Cite journal |last1=Christensen |first1=John Daniel |last2=Sinnamon |first2=Gordon |last3=Wu |first3=Enxin |date=2014-10-09 |title=The D -topology for diffeological spaces |url=http://www.msp.org/pjm/2014/272-1/p04.xhtml |journal=[[Pacific Journal of Mathematics]] |language=en |volume=272 |issue=1 |pages=87–110 |arxiv=1302.2935 |doi=10.2140/pjm.2014.272.87 |issn=0030-8730 |doi-access=free}}</ref> <ref name="Laub06">{{Cite journal |last=Laubinger |first=Martin |date=2006 |title=Diffeological spaces |url=https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/1542 |journal=Proyecciones |language= |volume=25 |issue=2 |pages=151–178 |doi=10.4067/S0716-09172006000200003 |issn=0717-6279 |doi-access=free}}</ref> <ref name="ChrWu14">{{Cite journal |last1=Christensen |first1=Daniel |last2=Wu |first2=Enxin |date=2016 |title=Tangent spaces and tangent bundles for diffeological spaces |url=https://cahierstgdc.com/wp-content/uploads/2017/11/ChristensenWu.pdf |journal=[[Cahiers de Topologie et Géométrie Différentielle Catégoriques]] |volume=57 |issue=1 |pages=3–50 |arxiv=1411.5425}}</ref> <ref name="Bloh24">{{Citation |last=Blohmann |first=Christian |title=Elastic diffeological spaces |date=2024 |work=Recent advances in diffeologies and their applications |volume=794 |issue= |pages=49–86 |editor-last=Magnot |editor-first=Jean-Pierre |url=https://www.ams.org/books/conm/794/ |access-date=2025-03-17 |series=Contemporary Mathematics |place= |publisher=[[American Mathematical Society]] |arxiv=2301.02583 |doi=10.1090/conm/794 |isbn=978-1-4704-7254-2}}</ref> <ref name="Nest21">{{Cite journal |last=van der Schaaf |first=Nesta |date=2021 |title=Diffeological Morita Equivalence |url=https://cahierstgdc.com/wp-content/uploads/2021/04/Van-der-Schaaf-_LXII-2.pdf |journal=[[Cahiers de Topologie et Géométrie Différentielle Catégoriques]] |volume=LXII |issue=2 |pages=177–238 |arxiv=2007.09901}}</ref> <ref name="GurIgl19">{{Cite journal |last1=Gürer |first1=Serap |last2=Iglesias-Zemmour |first2=Patrick |date=2019 |title=Differential forms on manifolds with boundary and corners |journal=[[Indagationes Mathematicae]] |language=en |volume=30 |issue=5 |pages=920–929 |doi=10.1016/j.indag.2019.07.004 |doi-access=free}}</ref> <ref name="Hain79">{{Cite journal |last=Hain |first=Richard M. |date=1979 |title=A characterization of smooth functions defined on a Banach space |url=https://www.ams.org/proc/1979-077-01/S0002-9939-1979-0539632-8/ |journal=[[Proceedings of the American Mathematical Society]] |language=en |volume=77 |issue=1 |pages=63–67 |doi=10.1090/S0002-9939-1979-0539632-8 |issn=0002-9939 |doi-access=free}}</ref> <ref name="Los92">{{Cite journal |last=Losik |first=Mark |date=1992 |title=О многообразиях Фреше как диффеологических пространствах |trans-title=Fréchet manifolds as diffeological spaces |url=http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=ivm&paperid=4812&option_lang=eng |journal=Izv. Vyssh. Uchebn. Zaved. Mat. |language=ru |volume=5 |pages=36–42 |via=[[All-Russian Mathematical Portal]]}}</ref> <ref name="Los94">{{Cite journal |last=Losik |first=Mark |date=1994 |title=Categorical differential geometry |url=http://www.numdam.org/item/CTGDC_1994__35_4_274_0/ |journal=[[Cahiers de Topologie et Géométrie Différentielle Catégoriques]] |volume=35 |issue=4 |pages=274–290}}</ref> <ref name="FrolKrieg88">{{Cite book |last1=Frölicher |first1=Alfred |author-link1=Alfred Frölicher |title=Linear spaces and differentiation theory |last2=Kriegl |first2=Andreas |date=1988 |publisher=[[Wiley (publisher)|J. Wiley & sons]] |isbn=978-0-471-91786-1 |series=Pure and applied mathematics |location=Chichester |language=en}}</ref> <ref name="Miy25">{{Citation |last=Miyamoto |first=David |title=Lie algebras of quotient groups |date=2025-02-14 |url=https://arxiv.org/abs/2502.10260 |access-date=2025-03-21 |publisher= |arxiv=2502.10260 |id=}}</ref> <ref name="IglKarZad10">{{Cite journal |last1=Iglesias-Zemmour |first1=Patrick |last2=Karshon |first2=Yael |last3=Zadka |first3=Moshe |date=2010 |title=Orbifolds as diffeologies |url=https://www.ams.org/journals/tran/2010-362-06/S0002-9947-10-05006-3/S0002-9947-10-05006-3.pdf |journal=[[Transactions of the American Mathematical Society]] |volume=362 |issue=6 |pages=2811–2831 |doi=10.1090/S0002-9947-10-05006-3 |jstor=25677806 |s2cid=15210173}}</ref> <ref name="Miy24">{{Citation |last=Miyamoto |first=David |title=Lie groupoids determined by their orbit spaces |date=2024-03-22 |url=https://arxiv.org/abs/2310.11968 |access-date=2025-03-21 |publisher= |arxiv=2310.11968 |id=}}</ref> <ref name="DonIgl85">{{Cite journal |last1=Donato |first1=Paul |last2=Iglesias |first2=Patrick |date=1985 |title=Exemples de groupes difféologiques: flots irrationnels sur le tore |trans-title=Examples of diffeological groups: irrational flows on the torus |journal=[[Comptes rendus de l'Académie des Sciences|C. R. Acad. Sci. Paris Sér. I]] |language=fr |volume=301 |issue=4 |pages=127–130 |mr=799609}}</ref> <ref name="KarMiyWat24">{{Cite journal |last1=Karshon |first1=Yael |last2=Miyamoto |first2=David |last3=Watts |first3=Jordan |date=2024-10-01 |title=Diffeological submanifolds and their friends |url=https://linkinghub.elsevier.com/retrieve/pii/S0926224524000639 |journal=Differential Geometry and Its Applications |volume=96 |pages=102170 |arxiv=2204.10381 |doi=10.1016/j.difgeo.2024.102170 |issn=0926-2245}}</ref> <ref name="Jor82">{{Cite journal |last=Joris |first=Henri |date=1982-09-01 |title=Une C∞-application non-immersive qui possède la propriété universelle des immersions |trans-title=A non-immersive C∞-map which possesses the universal property of immersions |url=https://doi.org/10.1007/BF01899535 |journal=[[Archiv der Mathematik]] |language=fr |volume=39 |issue=3 |pages=269–277 |doi=10.1007/BF01899535 |issn=1420-8938}}</ref> <ref name="Ham82">{{cite journal |last1=Hamilton |first1=Richard S. |author-link=Richard S. Hamilton |title=The inverse function theorem of Nash and Moser |url = https://www.ams.org/journals/bull/1982-07-01/S0273-0979-1982-15004-2/S0273-0979-1982-15004-2.pdf |journal=[[Bulletin of the American Mathematical Society]] |date=1982 |volume=7 |issue=1 |pages=65–222 |doi=10.1090/S0273-0979-1982-15004-2}}</ref> <ref name="Wal12">{{cite journal |last1=Waldorf |first1=Konrad |title=Transgression to loop spaces and its inverse, I: Diffeological bundles and fusion maps |journal=[[Cahiers de Topologie et Géométrie Différentielle Catégoriques]] |date=2012 |volume=53 |issue=3 |pages=162–210 |issn=2681-2363}}</ref> }}
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