Graded Extensions of Monoidal Categories
نویسندگان
چکیده
Graded monoidal categories were introduced by Frohlich and C.T.C. ̈ Wall in 8 , where they presented a suitable abstract setting to study the Brauer group in equivariant situations. This paper is concerned with the analysis and classification of these graded monoidal categories, following a parallel treatment to that made in 2 for the non-monoidal case. In any graded monoidal category, its 1-component, or subcategory of all morphisms of grade 1, inherits a monoidal structure, and the graded category can be regarded as an extension of that monoidal subcategory by the group of grades. In developing this point of view, we are led to the problem of extending monoidal categories by groups, that is, the classification and construction of the manifold of all graded monoidal categories, the type being given group with 1-component isomorphic to a given Ž . monoidal category C , . This problem, including the theory of obstruc-
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