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Bunge, Marta; Paré, Robert

Stacks and equivalence of indexed categories. (English) Zbl 0432.18003

Cah. Topol. Géom. Différ. 20, 373-399 (1979).
Reviewer: Hans Engenes (Gjövik
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Cited in 4 Reviews
Cited in 17 Documents

MSC:

18B25 Topoi
18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects)
18D35 Structured objects in a category (MSC2010)

Keywords:

indexed category; topos; site; Morita equivalence for category objects; stack completions

Citations:

Zbl 0389.18002
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\textit{M. Bunge} and \textit{R. Paré}, Cah. Topologie Géom. Différ. Catégoriques 20, 373--399 (1979; Zbl 0432.18003)
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References:

[1] 1 M. Barr , Exact categories, in Exact categories and categories of sheaves , Lecture Notes in Math. 236 , Springer ( 1970 ), 1 - 120 . Zbl 0223.18010 · Zbl 0223.18010
[2] 2 M. Bunge , Stack completions and Morita equivalence for categories in a topos , Cahiers Topo. et Géo. Diff. , same issue. Numdam | Zbl 0432.18004 · Zbl 0432.18004
[3] 3 J. Duskin , Variations on Beck’s tripleability criterion , in Reports of the Midwest Cat. Seminar III, Lecture Notes in Math. 106 , Springer ( 1969 ), 74 . MR 252471 | Zbl 0211.32501 · Zbl 0211.32501
[4] 4 J . Gir AUD, Cohomologie non abélienne , Springer , Berlin , 1971 . MR 344253 | Zbl 0226.14011 · Zbl 0226.14011
[5] 5 J. Giraud , Classifying topos , in Toposes, Algebraic Geometry and Logic , Lecture Notes in Math. 274 , Springer ( 1972 ), 43 - 56 . MR 349807 | Zbl 0267.18014 · Zbl 0267.18014
[6] 6 A. Grothendieck , Technique et descente et théorèmes d’existence en Géométrie Algébrique , Séminaire Bourbaki n^\circ 190 ( 1959 /60). Numdam | Zbl 0229.14007 · Zbl 0229.14007
[7] 7 R.P. Are & D. Schumacher , Abstract families and the adjoint functor Theorems , in Indexed categories and their applications , Lecture Notes in Math. 661 , Springer ( 1978 ), 1 - 125 . MR 514193 | Zbl 0389.18002 · Zbl 0389.18002
[8] 8 G. Wraith , Lecture on elementary topoi , in Model theory and Topoi , Lecture Notes in Math. 445 , Springer ( 1975 ), 114 - 206 . MR 393179 | Zbl 0323.18005 · Zbl 0323.18005
[9] 9 G. Wraith , Locally equivalent toposes , Manuscript, Univ. Sussex , 1977 . MR 577506 · Zbl 0432.18002
[10] 10 J. Benabou & J. Roubaud , Monades et descente , C. R. A. S. Paris 270 ( 1970 ), A, 96 - 98 . MR 255631 | Zbl 0287.18007 · Zbl 0287.18007
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