Distributions and heat equation in SDG
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 47 (2006) no. 1, pp. 2-28.
@article{CTGDC_2006__47_1_2_0,
     author = {Kock, Anders and Reyes, Gonzalo},
     title = {Distributions and heat equation in $SDG$},
     journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques},
     pages = {2--28},
     publisher = {Dunod \'editeur, publi\'e avec le concours du CNRS},
     volume = {47},
     number = {1},
     year = {2006},
     mrnumber = {2220059},
     zbl = {1098.58002},
     language = {en},
     url = {http://archive.numdam.org/item/CTGDC_2006__47_1_2_0/}
}
TY  - JOUR
AU  - Kock, Anders
AU  - Reyes, Gonzalo
TI  - Distributions and heat equation in $SDG$
JO  - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY  - 2006
SP  - 2
EP  - 28
VL  - 47
IS  - 1
PB  - Dunod éditeur, publié avec le concours du CNRS
UR  - http://archive.numdam.org/item/CTGDC_2006__47_1_2_0/
LA  - en
ID  - CTGDC_2006__47_1_2_0
ER  - 
%0 Journal Article
%A Kock, Anders
%A Reyes, Gonzalo
%T Distributions and heat equation in $SDG$
%J Cahiers de Topologie et Géométrie Différentielle Catégoriques
%D 2006
%P 2-28
%V 47
%N 1
%I Dunod éditeur, publié avec le concours du CNRS
%U http://archive.numdam.org/item/CTGDC_2006__47_1_2_0/
%G en
%F CTGDC_2006__47_1_2_0
Kock, Anders; Reyes, Gonzalo. Distributions and heat equation in $SDG$. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 47 (2006) no. 1, pp. 2-28. http://archive.numdam.org/item/CTGDC_2006__47_1_2_0/

[1] Artin, M., Grothendieck, A. and Verdier, J.-L., Théorie des Topos (SGA 4), Springer LNM 269 (1972). | MR

[2] Chen, K.T. Iterated integrals of differential forms and loop space homology, Annals of Math. (2) 97 (1972), 217-146. | MR | Zbl

[3] Dubuc, E., Sur les modèles de la géométrie différentielle synthétique, Cahiers de Topologie et Géometrie Diff. 20 (1979), 231-279. | Numdam | MR | Zbl

[4] Frölicher, A., Cartesian Closed Categories and Analysis of Smooth Maps, in "Categories in Continuum Physics", Buffallo 1982 (ed. F.W. Lawvere and S.H. Schanuel), Springer Lecture Notes in Math. 1174 (1986). | MR | Zbl

[5] Frölicher, A., Kriegl, A., Linear Spaces and Differentiation Theory, Wiley 1988. | MR | Zbl

[6] Kelley, J.L., General Topology, Van Nostrand 1955. | MR | Zbl

[7] Kelley, J.L., Namioka, I., and Co-Authors, Linear Topological Spaces, Van Nostrand 1963. | MR | Zbl

[8] Kock, A. Properties of well-adapted models for synthetic differential geometry, Joum. Pure Appl. Alg. 20 (1981), 55-70. | MR | Zbl

[9] Kock, A., Synthetic Differential Geometry, Cambridge University Press 1981. | MR | Zbl

[10] Kock, A., Calculus of smooth functions between convenient vector spaces, Aarhus Preprint Series 1984/85 No. 18. Retyped in http://home.imf.au.dk/kock/CSF.pdf

[11] Kock, A., Convenient vector spaces embed into the Cahiers topos, Cahiers de Topologie et Géométrie Diff. Catégoriques 27 (1986), 3-17. | EuDML | Numdam | MR | Zbl

[12] Kock, A. and Reyes, G.E., Models for synthetic integration theory, Math. Scand. 48 (1981), 145-152. | EuDML | MR | Zbl

[13] Kock, A. and Reyes, G.E., Corrigendum and addenda to "Convenient vector spaces embed", Cahiers de Topologie et Géométrie Diff. Catégoriques 28 (1987), 99-110. | EuDML | Numdam | MR | Zbl

[14] Kock, A. and Reyes, G.E., Some calculus with extensive quantities: wave equation, Theory and Applications of Categories, Vol. 11 (2003), No. 14. | EuDML | MR | Zbl

[15] Kriegl, A. and Michor, P., The Convenient Setting of Global Analysis, Amer. Math. Soc. 1997. | MR | Zbl

[16] Lavendhomme, R., Basic Concepts of Synthetic Differential Geometry, Kluwer Acad. Publishers 1996. | MR | Zbl

[17] Lawvere, F.W., Catgeories of Space and of Quantity, in "The Space of Mathematics. Philosophical, Epistemological and Historical Explorations", DeGruyter, Berlin 1992, 14-30. | MR | Zbl

[18] Lawvere, F.W., Volterra's Functionals and Covariant Cohesion of Space, Rendiconti del Circolo Mat. di Palermo Serie II, Suppl. 64 (2000), 201-214. | MR | Zbl

[19] Losik, M.V. Frechet manifolds as diffeological spaces, Soviet Math. (Iz. vuz) 5 (1992), 36-42. | MR | Zbl

[20] Moerdijk, I. and and Reyes, G.E., Models for Smooth Infinitesimal Analysis, Springer 1991. | MR | Zbl

[21] Nel, L.D., Enriched locally convex structures, Differential Calculus and Riesz representations, Joum. Pure Appl. Alg. 42 (1986), 165-184. | MR | Zbl

[22] Porta, H. and Reyes, G.E., Variétés à bord et topos lisse, in "Analyse dans les topos lisses" (ed. G.E. Reyes), Rapport de Rechercehes D.M.S. 80-12, Université de Montréal 1980. | MR

[23] Quê, N.V. and Reyes, G.E. Théorie des distribution et théorème d'extension de Whitney, in "Analyse dans les topos lisses" (ed. G.E. Reyes), Rapport de Rechercehes D.M.S. 80-12, Université de Montréal 1980.

[24] Reyes, G.E., A model of SDG in which only trivial distributions with compact support have a density, in http://reyes-reyes.com/gonzalo/recent_work/syntheticdifferential/

[25] Reyes, G.E., Embedding manifolds with boundary in smooth toposes, in http://reyes-reyes.com/gonzalo/recent_work/syntheticdifferential/ [26]

[26] Schwartz, L., Théorie des distributions, Tome 1, Hermann Paris 1957. | MR | Zbl

[27] Schwartz, L., Méthodes mathématiques pour les sciences physiques, Hermann Paris 1961. | MR | Zbl

[28] Seeley, R.T., Extension of C∞ functions defined in a half space, Proc. Amer. Math. Soc. 15 (1964), 625-626. | Zbl