Generalized logic and the representation of rings |
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Authors: | Simon Ambler Dominic Verity |
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Affiliation: | (1) University of Leicester, LE1 7RH Leicester, England;(2) Macquarie University, 2109, New South Wales, Australia |
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Abstract: | Following the progression towards weaker logics, a number of authors have considered the notion of a sheaf over a quantale or, equivalently, a quantale valued set. In this paper, we use ideas from enriched category theory to motivate the definition of a quantic sheaf. Given a localic subquantale of Q, a quantic sheaf over Q gives a sheaf in the usual sense. As an application, we derive a series of sheaf representations for commutative rings including the familiar Pierce representation. |
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Keywords: | quantale enriched category quantic sheaf ring representation |
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