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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex-geometry computable-mathematics computer-science connection constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry goodwillie-calculus graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory history homological homological-algebra homology homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie lie-theory limit limits linear linear-algebra locale localization logic mathematics measure-theory modal-logic model model-category-theory monoidal monoidal-category-theory morphism motives motivic-cohomology nonassociative noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pasting philosophy physics planar pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthormikestay
   • CommentTimeJul 13th 2017
   • PermaLink
   Author: mikestay
   Format: MarkdownItexThe article says, "if [commuting square involving $A,B,C,D,e,j,u,v$] is a commutative diagram with $e$ bijective on objects and $s$ essentially surjective, then there is a unique functor $h \colon B\to C$ such that $h e = u$ and $j h = v$." The symbol $s$ is never used in the diagram; should it be "$j$ fully faithful" instead of "$s$ essentially surjective"?

   The article says, “if [commuting square involving $A,B,C,D,e,j,u,v$] is a commutative diagram with $e$ bijective on objects and $s$ essentially surjective, then there is a unique functor $h \colon B\to C$ such that $h e = u$ and $j h = v$.” The symbol $s$ is never used in the diagram; should it be “$j$ fully faithful” instead of “$s$ essentially surjective”?

2. • CommentRowNumber2.
   • CommentAuthormikestay
   • CommentTimeJul 13th 2017
   • PermaLink
   Author: mikestay
   Format: MarkdownItex[link to article](https://ncatlab.org/nlab/show/%28bo%2C+ff%29+factorization+system)

   link to article

3. • CommentRowNumber3.
   • CommentAuthorTodd_Trimble
   • CommentTimeJul 13th 2017
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   Author: Todd_Trimble
   Format: MarkdownItexYeah, weird. I changed it.

   Yeah, weird. I changed it.