Graded Monoidal Categories Compositio Mathematica, Tome 28, No 3 (1974), P
COMPOSITIO MATHEMATICA A. FRÖHLICH C. T. C. WALL Graded monoidal categories Compositio Mathematica, tome 28, no 3 (1974), p. 229-285 <http://www.numdam.org/item?id=CM_1974__28_3_229_0> © Foundation Compositio Mathematica, 1974, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions géné- rales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infrac- tion pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ COMPOSITIO MATHEMATICA, Vol. 28, Fasc. 3, 1974, pag. 229-285 Noordhoff International Publishing Printed in the Netherlands GRADED MONOIDAL CATEGORIES A. Fröhlich and C. T. C. Wall Introduction This paper grew out of our joint work on the Brauer group. Our idea was to define the Brauer group in an equivariant situation, also a ’twisted’ version incorporating anti-automorphisms, and give exact sequences for computing it. The theory related to representations of groups by auto- morphisms of various algebraic structures [4], [5], on one hand, and to the theory of quadratic and Hermitian forms (see particularly [17]) on the other. In developing these ideas, we observed that many of the arguments could be developed in a purely abstract setting, and that this clarified the nature of the proofs. The purpose of this paper is to present this setting, together with such theorems as need no further structure. To help motivate the reader, and fix ideas somewhat in tracing paths through the abstractions which follow, we list some of the examples to which the theory will be applied.
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