The category of complete Boolean algebras is not an intersection of reflective subcategories of the category of frames |
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Authors: | V Vajner |
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Institution: | (1) Department of Mathematics, University of Cape Town, Private Bag, 7700 Rondebosch, South Africa |
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Abstract: | We answer a question of J. Rosický and W. Tholen by showing that the class of complete Boolean algebras (which is a prereflective subcategory of the category of frames) is not an intersection of reflective subcategories of the category of frames. In order to deduce this result, we first prove the following observation (using some basic facts about congruence frames): the three-element chain belongs to every reflective subcategory of the category of frames which contains the class of complete Boolean algebras.Supported by the Categorical Topology Research Group at the University of Cape Town, under funding from the Foundation for Research Development and the University of Cape Town. |
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Keywords: | Reflective subcategory frame complete Boolean algebra |
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