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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry 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 homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics 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 sheaves simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeNov 2nd 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexThis entry had a section "Abuses" (originating in [rev 1](https://ncatlab.org/nlab/revision/cofinal+diagrams/1)) which contained exactly the following paragraph: > It is often said that two diagrams are cofinal even when neither has a colimit, if they acquire a common colimit on passing to a suitable completion of $C$. This can probably be phrased internally to $C$, at the cost of intuition. I am hereby removing this section for the time being. Maybe there is something to be said here, but the headline "Abuses" seems disconnected from what the paragraph says, the first sentence remains vague and the second and last sentence seems to call into question whether the author of these lines had thought this through. If anyone knows what useful statement the author of these lines had in mind, let's sort it out, phrase it clearly, and then add it back to the entry. <a href="https://ncatlab.org/nlab/revision/diff/cofinal+diagrams/6">diff</a>, <a href="https://ncatlab.org/nlab/revision/cofinal+diagrams/6">v6</a>, <a href="https://ncatlab.org/nlab/show/cofinal+diagrams">current</a>

   This entry had a section “Abuses” (originating in rev 1) which contained exactly the following paragraph:

   It is often said that two diagrams are cofinal even when neither has a colimit, if they acquire a common colimit on passing to a suitable completion of $C$. This can probably be phrased internally to $C$, at the cost of intuition.

   I am hereby removing this section for the time being. Maybe there is something to be said here, but the headline “Abuses” seems disconnected from what the paragraph says, the first sentence remains vague and the second and last sentence seems to call into question whether the author of these lines had thought this through.

   If anyone knows what useful statement the author of these lines had in mind, let’s sort it out, phrase it clearly, and then add it back to the entry.

   diff, v6, current