nLab (eso and full, faithful) factorization system




In the 2-topos Cat, the pair of classes of morphisms

forms 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 2-exact 2-category and any (2,1)-exact (2,1)-category, including any Grothendieck 2-topos or (2,1)-topos; see here.


More on this is at infinity-image – Of Functors between groupoids.

Last revised on May 27, 2020 at 16:45:18. See the history of this page for a list of all contributions to it.