Projectivity, continuity and adjointness: quantales, Q-posets and Q-modules

Susan Niefield

In this paper, projective modules over a quantale are characterized by distributivity, continuity, and adjointness conditions. It is then shown that a morphism Q --> A of commutative quantales is coexponentiable if and only if the corresponding Q-module is projective, and hence, satisfies these equivalent conditions.

Keywords: projective, flat, completely distributive, totally continuous, quantale module

2010 MSC: 06F07,18A40,18D10,18D20

Theory and Applications of Categories, Vol. 31, 2016, No. 30, pp 839-851.

Published 2016-09-26.

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