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On regular presheaves and regular semi-categories. (English) Zbl 1038.18006
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.

MSC:
18D20 Enriched categories (over closed or monoidal categories)
16D90 Module categories in associative algebras
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References:
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