The Orthogonal Subcategory Problem and the Small Object Argument

@article{Admek2009TheOS,
  title={The Orthogonal Subcategory Problem and the Small Object Argument},
  author={Jir{\'i} Ad{\'a}mek and Michel H{\'e}bert and Lurdes Sousa},
  journal={Applied Categorical Structures},
  year={2009},
  volume={17},
  pages={211-246}
}
Our paper is devoted to two classical problems of category theory: the Orthogonal Subcategory Problem which asks, given a class H of morphisms, whether the subcategory H⊥ of all objects orthogonal to every member of H is reflective. And the Small Object Argument which asks whether the subcategory InjH of all objects injective to every member of H is weakly reflective and, moreover, the weak reflection maps can be chosen to be cellular (that is: they lie in the closure of H under transfinite… CONTINUE READING

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