Quantaloids and non-commutative ring representations
(1995) Applied Categorical Structures : a journal devoted to applications of categorical methods in algebra, analysis, order, topology and computer science — Vol. 3, n° 4, p. 305-320 (1995)
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- Abstract
- Our aim is to generalize to the non-commutative case, the generic representation of commutative rings by sheaves on their quantales of ideals. As the quantale of two-sided ideals is not a sufficiently rich structure, we define and work on a quantaloid of left and right ideals. A workable notion of sheaf is introduced using matrices with values in a quantaloid. For a given ring R, we obtain a category of sheaves where the terminal object is endowed with a special subobject. There exists a representing sheaf for R in the sense that the elements of R correspond to the sections from the special subobject and the global sections correspond to the center.
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Citations
Vandenbossche, G. (1995). Quantaloids and non-commutative ring representations. Applied Categorical Structures : a journal devoted to applications of categorical methods in algebra, analysis, order, topology and computer science, 3(4), 305-320. https://doi.org/10.1007/BF00872902 (Original work published 1995)