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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 definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration 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 nforum 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 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
   • CommentTimeJun 14th 2018
   • (edited Jun 14th 2018)
   • PermaLink
   Author: Urs
   Format: MarkdownItexgave this statement its own entry, as it is being referenced or used in a variety of other entries. Also spelled out a proof. Not a short one but, hopefully, a conceptual one. <a href="https://ncatlab.org/nlab/revision/categories+with+finite+products+are+cosifted/1">v1</a>, <a href="https://ncatlab.org/nlab/show/categories+with+finite+products+are+cosifted">current</a>

   gave this statement its own entry, as it is being referenced or used in a variety of other entries. Also spelled out a proof. Not a short one but, hopefully, a conceptual one.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorDylan Wilson
   • CommentTimeJun 14th 2018
   • PermaLink
   Author: Dylan Wilson
   Format: MarkdownItexMaybe a quicker proof: By Quillen's theorem A, you need to show that $C_{/(x,y)}$ is contractible; but it has a final object! So you're done.

   Maybe a quicker proof: By Quillen’s theorem A, you need to show that $C_{/(x,y)}$ is contractible; but it has a final object! So you’re done.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJun 14th 2018
   • PermaLink
   Author: Urs
   Format: MarkdownItexFeel invited to add other proofs to the entry!

   Feel invited to add other proofs to the entry!