Moens, M.-A.; Berni-Canani, U.; Borceux, F. On regular presheaves and regular semi-categories. (English) Zbl 1038.18006 Cah. Topol. Géom. Différ. Catég. 43, No. 3, 163-190 (2002). Regular modules play an essential role in the construction of the Brauer-Taylor group of a ring via the consideration of Azumaya algebras without unit. In [F. Borceux and E. Vitale, Appl. Categ. Struct. 10, 449–467 (2002; Zbl 1033.18005)] Azumaya categories enriched in a symmetrical monoidal closed category have been introduced which enjoy the categorical Brauer group. This paper aims at an analogous theory “without identities” with enriched Azumaya graphs and the corresponding categorical Brauer-Taylor group of the base category. Investigations on the properties of the notions introduced here are relegated to a subsequent paper. Reviewer: Hirokazu Nishimura (Tsukuba) Cited in 4 Documents MSC: 18D20 Enriched categories (over closed or monoidal categories) 16D90 Module categories in associative algebras Keywords:regular module; Yoneda lemma; semi-category Citations:Zbl 1033.18005 PDFBibTeX XMLCite \textit{M. A. Moens} et al., Cah. Topol. Géom. Différ. Catég. 43, No. 3, 163--190 (2002; Zbl 1038.18006) Full Text: Numdam EuDML References: [1] F. Borceux , A handbook of categorical algebra ( 3 volumes), Cambridge University Press , 1994 MR 1315049 | Zbl 0911.18001 · Zbl 0911.18001 [2] F. Borceux and E. Vitale , Azumay a categories , 21 pages, to appear in ” Applied categorical structures ” MR 1937232 | Zbl 1033.18005 · Zbl 1033.18005 [3] F. Grandjean and E. Vitale , Morita equivalence for regular algebras, Cahiers de Topologie et Géométrie Différentielle Catégorique , 39 - 2 , 1998 , 137 - 153 Numdam | MR 1631300 | Zbl 0919.16005 · Zbl 0919.16005 [4] D. Higgs , Injectivity in the topos of complete Heyting valued sets , Can. J. Math. 36 - 3 , 1984 , 550 - 568 MR 752984 | Zbl 0541.18003 · Zbl 0541.18003 [5] G.M. Kelly , Basic concepts of enriched category theory , London Math. Soc. Lect. Notes 64 , 1982 , Cambridge University Press MR 651714 | Zbl 0478.18005 · Zbl 0478.18005 [6] G.M. Kelly and F.W. Lawvere , On the complete lattice of essential localizations , Bull. de la Soc. Math. de Belgique XLI- 2 , 1989 , 289 - 320 MR 1031753 | Zbl 0686.18005 · Zbl 0686.18005 [7] F.W. Lawvere , Unity and identity of opposites in calculus and physices Appl . Categorical Structures , 4 , 1996 , 167 - 174 , MR 1406096 | Zbl 0858.18002 · Zbl 0858.18002 [8] R. Schatten , Norm ideals of completely continuous operators , Ergebnisse de Math. und ihrer Grenzgebiete 27 , 1970 , Springer MR 257800 | Zbl 0188.44103 · Zbl 0188.44103 [9] J.L. Taylor , A bigger Brauer group , Pacific J. of Math. 103 - 1 , 1982 , 163 - 203 Article | MR 687968 | Zbl 0528.13007 · Zbl 0528.13007 [10] J. Weidmann , Linear operators in Hilbert spaces , Graduate Texts in Math. 68 , 1980 , Springer MR 566954 | Zbl 0434.47001 · Zbl 0434.47001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.