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19 pages, republished in: Reprints in Theory and Applications of Categories, No. 14 (2005), pp 1-18

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Originally published as: Enriched categories and cohomology, Quaestiones Mathematicae, 6 (1983), 265-283, used by permission. 2000 MSC: 18D20, 18D30 Republished in: Reprints in Theory and Applications of Categories, No. 14 (2005), pp 1-18 http://www.tac.mta.ca/tac/reprints/articles/14/tr14.dvi http://www.tac.mta.ca/tac/reprints/articles/14/tr14.ps http://www.tac.mta.ca/tac/reprints/articles/14/tr14.pdf TAC Reprints Home References [Ben1] J. Benabou, Introduction to bicategories, Lecture Notes in Math., 47 (Springer, Berlin,1967), 1-77. [Ben2] J. Benabou, Fibrations petites et localement petites, C.R. Acad. Sci. Paris Sr.A, 281 (1975), 897--900. [Bt1] R. Betti, Una teoria categoriale degli automi, Universita degli Studi di Milano, Instituto Mathematico F. Enriquesa, Quaderno n. 35/s (1979). ENRICHED CATEGORIES AND COHOMOLOGY 17 [Bt2] R. Betti, Bicategorie di base, Universta degli Studi di Milano, Istituto Mathematico F. Enriquesa, Quaderno n. 2/s (II) (1981). [BC] R. Betti and A. Carboni, Cauchy completion and associated sheaf, Universita degli Studi di Milano, Istituto Mathematico F. Enriquesa, Quaderno n. 5/p (II) (1981). [Bou] D. Bourn, Une autre propriete universelle pour le champ associee, Cahiers de Topologie et Geometrie Differentielle , XXI - 4 (1980), 403-410. [Bun] M. Bunge, Stack completions and Morita equivalence for categories in a topos, Cahiers de Topologie et Geometrie Differentielle , XX - 4 (1979), 401-436. [Day] B. Day, Limit spaces and closed span categories, Lecture Notes in Math., 420 (Springer, Berlin - N.Y.,1974), 65--74. [EK] S. Eilenberg and G.M. Kelly, Closed categories, Proc. Conf. Categorical Algebra at La Jolla, (Springer, Berlin - N.Y.,1966), 421--562. [Gir] J. Giraud, Cohomologie non abelienne, (Springer, Berlin,1971). [Law] F.W. Lawvere, Teoria delle categorie sopra un topos di base, Lecture Notes, Univ. of Perugia, (1973). [PS] R. Pare and D. Schumacher, Abstract families and the adjoint functor theorem, Lecture Notes in Math., 661 (Springer, Berlin, 1978), 1-125. [Pen] J. Penon, Categories localement internes, C. R. Acad. Sci. Paris Sr. A, 278 (1974),1577--1580. [St1] R.H. Street, Elementary cosmoi, Lecture Notes in Math., 420 (Springer, Berlin,1974), 134--180. [St2] R.H. Street, Cosmoi of internal categories, Transactions Amer. Math. Soc., 258 (1980), 271--318. [St3] R.H. Street, Two dimensional sheaf theory, J. Pure and Applied Algebra, 23(3), (1982), 251--270. [SW] R.H. Street and R.F.C. Walters, Yoneda structures on 2-categories, J. Algebra, 50 (1978), 350--379. [Wal] R.F.C. Walters, Sheaves on sites as Cauchy-complete categories, J. Pure and Applied Algebra, 24(1) (1982), 95--102. 18 ROSS STREET Department of Mathematics, Macquarie University NSW 2109, Australia Email: street@math.mq.edu.au This article may be accessed from http://www.tac.mta.ca/tac/reprints or by anonymous ftp at ftp://ftp.tac.mta.ca/pub/tac/html/tac/reprints/articles/14/tr14.{dvi,ps

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