The Brauer and Brauer-Taylor groups of a symmetric monoidal category

 Access to full text

 Full (PDF)

1. [1] Auslander B.: The Brauer group of a ringed space, J. Algebra4 (1966), pp. 220-273. Zbl0144.03401MR199213
2. [2] Auslander M.& Goldman O.: The Brauer group of a commutative ring, Trans. Amer. Math. Soc.97 (1960), pp. 367-409. Zbl0100.26304MR121392
3. [3] Barja Perez J.M.: Teoremas de Morita para triples en categorias cerradas, Alxebra20 (1978). Zbl0376.18004
4. [4] Bass H.: Topics in Algebraic K-Theory, Tata Institut of Fundamental Research, Bombay (1967). Zbl0226.13006
5. [5] Bass H.: Algebraic K-Theory, W.A. Benjamin Inc. (1968). Zbl0174.30302MR249491
6. [6] Borceux F.: Handbook of Categorical Algebra 2, Encyclopedia of Math.51, Cambridge University Press (1994). Zbl0843.18001MR1313497
7. [7] Borceux F. & Vitale E.M.: A Morita theorem in topology, Suppl. Rend. Circ. Mat. PalermoII-29 (1992), pp. 353-362. Zbl0781.06013MR1197179
8. [8] Borceux F. & Vitale E.M.: On the notion of bimodel for functorial semantics, Applied Categorical Structures2 (1994), pp. 283-295. Zbl0804.18003MR1285885
9. [9] Caenepeel S.: Etale cohomology and the Brauer group, to appear. Zbl0596.13006
10. [10] Dukarm J.: Morita equivalences of algebraic theories, Colloquium Mathematicum55 (1988) pp. 11-17. Zbl0669.18005MR964315
11. [11] Fernández Vilaboa J.M.: Grupes de Brauer y de Galois de un algebra de Hopf en una categoria cerrada, Alxebra42 (1985). Zbl0579.16004
12. [12] Fischer-Palmquist J.: The Brauer group of a closed category, Proc. Amer. Math. Soc.50 (1975), pp. 61-67. Zbl0268.18006MR393195
13. [13] Fischer-Palmquist J. & Palmquist P.H.: Morita contexts of enriched categories, Proc. Amer. Math. Soc.50 (1975), pp. 55-60. Zbl0268.18007MR419559
14. [14] Gabber O.: Some theorems on Azumaya algebras, L. N. in Math. 844, Springer-Verlag (1988). Zbl0472.14013MR611868
15. [15] González Rodríguez R.: La sucesión exacta ..., Ph. D. Thesis, Santiago de Compostela (1994). 
16. [16] Heller A.: Some exact sequences in algebraic K-theory, Topology3 (1965), pp. 389-408. Zbl0161.01507MR179229
17. [17] Kelly G.M.: Basic concepts of enriched category theories, London Math. Soc. L. N.64, Cambridge University Press (1982). Zbl0478.18005MR651714
18. [18] Kelly G.M. & Laplaza M.L.: Coherence for compact closed categories, J. Pure Appl. Algebra19 (1980), pp. 193-213. Zbl0447.18005MR593254
19. [19] Knus M.A. & Ojanguren M.: Théorie de Descente et Algèbres d'Azumaya, L. N. in Math389, Springer-Verlag (1974). Zbl0284.13002MR417149
20. [20] Lindner H.: Morita equivalences of enriched categories, Cahiers Top. Géo. Diff.XV-4 (1974), pp. 377-397. Zbl0319.18006MR399209
21. [21] Long F.W.: A generalization of Brauer group of graded algebras, Proc. London Math. Soc.29 (1974), pp. 237-256. Zbl0294.13003MR354753
22. [22] Long F.W.: The Brauer group of dimodule algebras, J. Algebra30 (1974), pp. 559-601. Zbl0282.16007MR357473
23. [23] López López M.P. & Villanueva Novoa E.: The Brauer group of the category (R, σ)-Mod, Proc. First Belgian-Spanish week on Algebra and Geometry (1988). 
24. [24] Mitchell B.: Separable algebroids, Memoirs A.M.S. vol. 57 n. 333 (1985). Zbl0588.18007MR804210
25. [25] Orzech M. & Small C.: The Brauer Group of a commutative Ring, L. N. in Pure and Appl. Math11, Marcel Dekker (1975). Zbl0302.13001MR457422
26. [26] Pareigis B.: Non additive ring and module theory IV: the Brauer group of a symmetric monoidal category, L. N. in Math. 549, Springer-Verlag (1976), pp. 112-133. Zbl0362.18011MR498794
27. [27] Raeburn I. & Taylor J.L.: The bigger Brauer group and étale cohomology, Pacific J. Math.119 (1985), pp. 445-463. Zbl0596.13006MR803128
28. [28] Schack S.D.: Bimodules, the Brauer group, Morita equivalence and cohomology, J. Pure Appl. Algebra80 (1992), pp. 315-325. Zbl0765.16002MR1170717
29. [29] Taylor J.L.: A bigger Brauer group, Pacific J. Math.103 (1982), pp. 163-203. Zbl0528.13007MR687968
30. [30] Verschoren A.The Brauer group of a quasi-affine schema, L. N. in Math.917, Springer-Verlag (1982), pp. 260-278. Zbl0484.16002MR657435
31. [31] Vitale E.M.: Monoidal categories for Morita theory, Cahiers Top. Géo. Diff. CatégoriquesXXXIII-4 (1992), pp. 331-343. Zbl0767.18009MR1197429
32. [32] Vitale E.M.: Groupe de Brauer et distributeurs, talk at Journée de Catégories et Géométrie, Dunkerque (1995). 
33. [33] Wall C.T.C.: Graded Brauer groups, J. Reine Angew. Math.213 (1964), pp.187-199. Zbl0125.01904MR167498
34. [34] Wraith G.: Algebraic Theories, Aarhus UniversityL. N. Series 22 (1970). Zbl0249.18013MR262334
35. [35] Zelinski D.: Brauer groups, L. N. in Pure and Appl. Math.26, Marcel Dekker (1977). MR444634

1. F. Grandjean, E. M. Vitale, Morita equivalence for regular algebras
2. M.-A. Moens, E. M. Vitale, Groupoids and the Brauer group