Abstract
We show that a quotient category of the category of all topological spaces and all open continuous mappings contains an isomorphic copy of every category as a full subcategory. We construct a functorF : K → K universal in the following sense: for every functorH : H 1 → H 2 (H 1,H 2 arbitrary) there exist full one-to-one functors φ i :H i → K such thatF o φ1 = φ2 oH (the construction proceeds in a more general setting of enriched categories).
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Trnková, V. Universalities. Appl Categor Struct 2, 173–185 (1994). https://doi.org/10.1007/BF00873298
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DOI: https://doi.org/10.1007/BF00873298