On Functors Which Are Lax Epimorphisms

  title={On Functors Which Are Lax Epimorphisms},
  author={Jir{\'i} Ad{\'a}mek and R Bashir and Manuela Sobral},
We show that lax epimorphisms in the category Cat are precisely the functors P : E −→ B for which the functor P ∗ : [B,Set] −→ [E,Set] of composition with P is fully faithful. We present two other characterizations. Firstly, lax epimorphisms are precisely the “absolutely dense” functors, i.e., functors P such that every object B of B is an absolute colimit of all arrows P (E) −→ B for E in E. Secondly, lax epimorphisms are precisely the functors P such that for every morphism f of B the… CONTINUE READING

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