Abstract
In a category \({\mathcal {C}}\) with an (\({\mathcal {E}}\),\({\mathcal {M}}\))-factorization structure for morphisms, we prove that any subclass \({\mathcal {N}}\) of \({\mathcal {M}}\) which is closed under pullbacks determines a transitive quasi-uniform structure on \({\mathcal {C}}\). In addition to providing a categorical characterization of all transitive quasi-uniform structures compatible with a topology, this result also permits us to establish a number of Galois connections related to quasi-uniform structures on \({\mathcal {C}}\). These Galois connections lead to the description of subcategories of \({\mathcal {C}}\) determined by quasi-uniform structures. Several examples considered at the end of the paper illustrate our results.
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Funding
The first author was supported by the Brno University of Technology (BUT) under the project MeMoV II No. CZ.02.2.69/0.0/0.0/18-053/0016962. The second author was supported by BUT from the Specific Research Project No. FSI-S-20-6187.
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The findings of the results were done by the two authors. The paper was written by the first author and the corrections after the first author have written the paper were discussed by the two authors. The two authors agreed to submit the paper after discussion.
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The first author acknowledges the support from the Brno University of Technology (BUT) under the project MeMoV II No. CZ.02.2.69/0.0/0.0/18-053/0016962. The second author acknowledges the support by BUT from the Specific Research Project No. FSI-S-20-6187.
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Iragi, M., Šlapal, J. Transitive quasi-uniform structures depending on a parameter. Aequat. Math. 97, 823–836 (2023). https://doi.org/10.1007/s00010-022-00937-8
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DOI: https://doi.org/10.1007/s00010-022-00937-8