On Functors Which Are Lax Epimorphisms

@inproceedings{Admek2001OnFW,
  title={On Functors Which Are Lax Epimorphisms},
  author={Jir{\'i} Ad{\'a}mek and R Bashir and Manuela Sobral},
  year={2001}
}
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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References

Publications referenced by this paper.
Showing 1-10 of 10 references

Finite Preorders and Topological Descent II, Preprint 00-33

  • G. Janelidze, M. Sobral
  • 2000
1 Excerpt

Finite Preorders and Topological Descent I, Preprint 99-10

  • G. Janelidze, M. Sobral
  • 1999
1 Excerpt

Modulated Bicategories

  • A. Carboni, S. Johnson, R. Street, D. Verity
  • Jour Pure Appl. Algebra 94
  • 1994
3 Excerpts

Density Presentations of Functors

  • B. J. Day
  • Bull. Austr. Math. Soc. 16
  • 1977
1 Excerpt

Fibrations and Yoneda’s Lemma in a 2-category

  • R. Street
  • in: Sydney Category Seminar, LNM 420,
  • 1974
1 Excerpt

Categories for the Working Mathematician, Springer-Verlag

  • S. MacLane
  • New York,
  • 1971
1 Excerpt

Epimorphisms and Dominions III

  • J. R. Isbell
  • Am. J. Math. 90
  • 1968
1 Excerpt

Isbell , Epimorphisms and Dominions III

  • R. J.
  • Am . J . Math .
  • 1967

Kelly , Basic Concepts of Enriched Category Theory

  • M. G.

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