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Cartesian closedness in categories with an idempotent closure operator and closed morphisms

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Abstract

Given a subobject-structured category \(\mathcal X\), we construct a new category whose objects are the pairs (X, c) where X is an \(\mathcal X\)-object and c is an idempotent, monotonic and extensive endomap of the subobject lattice of X, and whose morphisms between objects are the closed maps between the corresponding subobject lattices. We give a sufficient condition on \(\mathcal X\) for the new category to be cartesian closed.

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Acknowledgements

This work was supported by the Brno University of Technology from the Specific Research Program, project no. FSI-S-20-6187.

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  1. Institute of Mathematics, Brno University of Technology, Technická 2, 616 69, Brno, Czech Republic

    Josef Šlapal

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  1. Josef Šlapal
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Correspondence to Josef Šlapal.

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Šlapal, J. Cartesian closedness in categories with an idempotent closure operator and closed morphisms. Aequat. Math. 96, 129–136 (2022). https://doi.org/10.1007/s00010-020-00772-9

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  • DOI: https://doi.org/10.1007/s00010-020-00772-9

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