Abstract
We investigate the existence of injective hulls (with respect to the class of embeddings) in the categories Top 0/B of T0 topological fibre spaces over B. We prove that, if f:A→B has a restriction to the image injective in Top 0/f(A), (A,f) has an injective hull in Top 0/B if and only if f(A′) is locally closed in B, where A′ denotes the union of non-indiscrete fibres of f.
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Cagliari, F., Mantovani, S. Injective Hulls of T0 Topological Fibre Spaces. Applied Categorical Structures 11, 377–390 (2003). https://doi.org/10.1023/A:1024464032027
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DOI: https://doi.org/10.1023/A:1024464032027