Injectivity and sections

  title={Injectivity and sections},
  author={F. Cagliaria and S. Mantovanib},
  • F. Cagliaria, S. Mantovanib
  • Published 2005
We investigate injectivity in a comma-category C/B using the notion of the “object of sections” S(f ) of a given morphismf : X → B in C. We first obtain that f : X → B is injective inC/B if and only if the morphism〈1X, f 〉 : X → X×B is a section inC/B and the object S(f ) of sections of f is injective inC. Using this approach, we study injective objects f with respect to the class of embeddings in the categories ContL/B (AlgL /B) of continuous (algebraic) lattices over B. As a result, we obtain… CONTINUE READING

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