category theory

# Contents

## Definition

In the 2-topos Cat, the pair of classes of morphisms (essentially surjective functors, fully faithful functors) form a factorization system in a 2-category. This factorization system can also be restricted to the (2,1)-topos Grpd.

In fact, an analogous factorization system exists in any regular 2-category and any (2,1)-exact (2,1)-category, including any Grothendieck 2-topos or (2,1)-topos; see here?.

## References

• M. Dupont, Enrico Vitale, Proper factorization systems in 2-categories, Journal of pure and applied algebra, 179 (2003), pp.65-86

Revised on November 15, 2016 15:13:05 by Urs Schreiber (2.247.247.6)