Etendues and stacks as bicategories of fractions

Dorette A. Pronk

Compositio Mathematica (1996)

  • Volume: 102, Issue: 3, page 243-303
  • ISSN: 0010-437X

How to cite

top

Pronk, Dorette A.. "Etendues and stacks as bicategories of fractions." Compositio Mathematica 102.3 (1996): 243-303. <http://eudml.org/doc/90454>.

@article{Pronk1996,
author = {Pronk, Dorette A.},
journal = {Compositio Mathematica},
keywords = {-spaces; bicategory of fractions; 2-category of toposes; étale groupoids; weak equivalences; equivalence of bicategories; differentiable stacks; schemes; algebraic stacks; étendues},
language = {eng},
number = {3},
pages = {243-303},
publisher = {Kluwer Academic Publishers},
title = {Etendues and stacks as bicategories of fractions},
url = {http://eudml.org/doc/90454},
volume = {102},
year = {1996},
}

TY - JOUR
AU - Pronk, Dorette A.
TI - Etendues and stacks as bicategories of fractions
JO - Compositio Mathematica
PY - 1996
PB - Kluwer Academic Publishers
VL - 102
IS - 3
SP - 243
EP - 303
LA - eng
KW - -spaces; bicategory of fractions; 2-category of toposes; étale groupoids; weak equivalences; equivalence of bicategories; differentiable stacks; schemes; algebraic stacks; étendues
UR - http://eudml.org/doc/90454
ER -

References

top
  1. Artin, M.: Algebraic Spaces, Yale Math. Monographs3, Yale University Press, 1971. Zbl0226.14001MR407012
  2. Artin, M.: Versal deformations and algebraic stacks, Inventiones Mathematicae27 (1974) 165-189. Zbl0317.14001MR399094
  3. Bénabou, J.: Introduction to bicategories, in Reports of the Midwest Category Seminar, L.N.M.47, 1-77, Springer-Verlag, New York, 1967. MR220789
  4. Bunge, M.: An application of descent to a classification theorem for toposes, Math. Proc. Camb. Phil. Soc.107-59(1990)59-79. Zbl0698.18003MR1021873
  5. Deligne, P. and Mumford, D.: The irreducibility of the spaces of curves of given genus, Publ. Math. I.H.E.S. 36 (1969) 75-109. Zbl0181.48803MR262240
  6. Faltings, G. and Chai, C.L.: Degeneration of Abelian Varieties, Springer-Verlag, New York, 1990. Zbl0744.14031MR1083353
  7. Gabriel, P. and Zisman, M.: Calculus of Fractions and Homotopy Theory, Springer-Verlag, New York, 1967. Zbl0186.56802MR210125
  8. Grothendieck, A. and Verdier, J.L.: Seminaire de Géometrie Algébrique IV, L.N.M.296, Springer-Verlag, New York, 1972. MR354653
  9. Johnstone, P.T.: Topos Theory, Academic Press, London, 1977. Zbl0368.18001MR470019
  10. Joyal, A. and Tierney, M.: An extension of the Galois theory of Grothendieck, Memoirs of the A.M.S., Vol. 51, Nr. 309,1984. Zbl0541.18002MR756176
  11. Kelly, G.M.: On Maclane's conditions for coherence of natural associativities, commutativities, etc., Journal of Algebra1 (1964) 397-402. Zbl0246.18008MR182649
  12. Knutson, D.: Algebraic Spaces, L.N.M. 203, Springer-Verlag, New York, 1971. Zbl0221.14001MR302647
  13. Maclane, S.: Categories for the Working Mathematician, Springer-Verlag, New York, 1971. Zbl0705.18001MR354798
  14. Milne, J.S.: Etale Cohomology, Princeton University Press, Princeton, New Jersey, 1980. Zbl0433.14012MR559531
  15. Moerdijk, I.: Toposes and groupoids, in Categorical Algebra and its Applications (ed. F. Borceux), L.N.M.1348, Springer-Verlag, New York, 1988,280-298. Zbl0659.18008MR975977
  16. Moerdijk, I.: The classifying topos of a continuous groupoid. I, Transactions of the A.M.S.310-2 (1988) 629-668. Zbl0706.18007MR973173
  17. Moerdijk, I.: Descent theory for toposes, Bulletin de la Société Mathématique de Belgique (série A) tome XLI Fasc. 2 (1989) 373-391. Zbl0688.18003MR1031756
  18. Moerdijk, I.: The classifying topos of a continuous groupoid. II, Cah. de top. et Géom. Diff. Cat.31-2 (1990) 137-168. Zbl0717.18001MR1080241
  19. Moerdijk, I.: Classifying toposes and foliations, Ann. Inst. Fourier41, Grenoble (1991) 189-209. Zbl0727.57029MR1112197
  20. Moerdijk, I.: Foliations, groupoids and Grothendieck étendues, Publ. del Sem. Mat. Garcia de Galdeano, serie II, no. 17 (1993), Universidad de Zaragoza. Zbl0804.57014MR1268130
  21. Rosenthal, K.: Etendues and categories with monic maps, J. Pure and Appl. Algebra22 (1981) 193-212. Zbl0473.18004MR624572
  22. Serre, J.-P.: Lie Algebras and Lie Groups, reprinted as L.N.M. 1500, Springer-Verlag, New York, 1992. Zbl0742.17008MR1176100

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.