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An outline of non-Abelian cohomology in a topos. I: The theory of bouquets and gerbes. (English) Zbl 0496.18009


MSC:

18G50 Nonabelian homological algebra (category-theoretic aspects)
18B25 Topoi
18D30 Fibered categories
18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories)
18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects)
18D35 Structured objects in a category (MSC2010)
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References:

[1] A Rtin , M. , Grothendieck topologies , Lecture Notes Harvard Univ. 1962 . Zbl 0208.48701 · Zbl 0208.48701
[2] Barr , M. , Grillet , P. & Van Osdol , D. , Exact categories and categories of sheaves , Lecture Notes in Math. 236 ( 1971 ), Springer . Zbl 0223.18009 · Zbl 0223.18009
[3] Bunge , M. , Essential points and stack completions , Preprint Mc Gill Univ. , 1979 . · Zbl 0432.18004
[4] Dem Azure , M. , Topologies et faisceaux, SGA 3, Exposé IV , Lecture Notes in Math. 151 , Springer ( 1970 ).
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[7] Giraud , J. , Méthode de la descente , Bull. Soc. Math. France 90 ( 1962 ), 323 - 448 . Numdam | Zbl 0211.32902 · Zbl 0211.32902
[8] Grothendieck , A. , Techniques de construction en Géométrie Analytique IV , Sém. H. Cartan ( 1960 /61), Exposé 11 , E.N.S. Paris , 1962 .
[9] Grothendieck , A. , Technique de descente et théorèmes d’existence en Géométrie Algébrique I , Séminaire Bourbaki 12 e année, Exp. 190. Paris ( 1959 ). Numdam · Zbl 0229.14007
[10] Grothendieck , A. , Catégories fibrées et descente, SGA I, Exposé VI , Lecture Notes in Math. 224 , Springer ( 1971 ).
[11] Johnstone , P. , Topos theory, London Math. Soc. Monog . 10 , Acad. Press 1977 . Zbl 0368.18001 · Zbl 0368.18001
[12] Joyal , A. , Private lecture , SU N Y at Buffalo , December 1974 .
[13] Penon , J. , Private letter of 26 July 1979 .
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