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The family approach to total cocompleteness and toposes. (English) Zbl 0512.18001

MSC:
18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)
18A32 Factorization systems, substructures, quotient structures, congruences, amalgams
18B25 Topoi
18F10 Grothendieck topologies and Grothendieck topoi
18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects)
18E10 Abelian categories, Grothendieck categories
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[1] Théorie des topos et cohomologie étale des schémas. Tome 2, Lecture Notes in Mathematics, Vol. 270, Springer-Verlag, Berlin-New York, 1972 (French). Séminaire de Géométrie Algébrique du Bois-Marie 1963 – 1964 (SGA 4); Dirigé par M. Artin, A. Grothendieck et J. L. Verdier. Avec la collaboration de N. Bourbaki, P. Deligne et B. Saint-Donat. · Zbl 0234.00007
[2] M. Barr, Exact categories, Lecture Notes in Math., vol. 236, Springer-Verlag, Berlin and New York, 1971, pp. 1-120. · Zbl 0223.18010
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[8] Ross Street and Robert Walters, Yoneda structures on 2-categories, J. Algebra 50 (1978), no. 2, 350 – 379. · Zbl 0401.18004 · doi:10.1016/0021-8693(78)90160-6 · doi.org
[9] Rosanna Succi Cruciani, La teoria delle relazioni nello studio di categorie regolari e di categorie esatte, Riv. Mat. Univ. Parma (4) 1 (1975), 143 – 158. · Zbl 0356.18004
[10] Walter Tholen, Note on total categories, Bull. Austral. Math. Soc. 21 (1980), no. 2, 169 – 173. · Zbl 0431.18002 · doi:10.1017/S0004972700005992 · doi.org
[11] R. F. C. Walters, Sheaves on sites as Cauchy-complete categories, J. Pure Appl. Algebra 24 (1982), no. 1, 95 – 102. · Zbl 0497.18016 · doi:10.1016/0022-4049(82)90061-5 · doi.org
[12] R. J. Wood, Some remarks on total categories, J. Algebra 75 (1982), no. 2, 538 – 545. · Zbl 0504.18001 · doi:10.1016/0021-8693(82)90055-2 · doi.org
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