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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 nlab noncommutative noncommutative-geometry number-theory object 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.
   • CommentAuthorMike Shulman
   • CommentTimeJan 3rd 2012
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexI noticed that some Anonymous Coward had created a very stubby stub at [[two-out-of-six property]], and used it as a place to put proofs of two theorems about when the 2-out-of-6 property is equivalent to saturation of the class of weak equivalences.

   I noticed that some Anonymous Coward had created a very stubby stub at two-out-of-six property, and used it as a place to put proofs of two theorems about when the 2-out-of-6 property is equivalent to saturation of the class of weak equivalences.

2. • CommentRowNumber2.
   • CommentAuthornLab edit announcer
   • CommentTimeMar 26th 2020
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexAdded the source *Cofibrations in Homotopy Theory*, which contains in Theorem 7.2.7 also a good discussion about 2-out-of-6, retracts and saturation in the context of cofibration categories. Anonymous <a href="https://ncatlab.org/nlab/revision/diff/two-out-of-six+property/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/two-out-of-six+property/4">v4</a>, <a href="https://ncatlab.org/nlab/show/two-out-of-six+property">current</a>

   Added the source Cofibrations in Homotopy Theory, which contains in Theorem 7.2.7 also a good discussion about 2-out-of-6, retracts and saturation in the context of cofibration categories.

   Anonymous

   diff, v4, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJul 24th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexHave made more explicit (now [here](https://ncatlab.org/nlab/show/two-out-of-six+property#ModelCategoriesSatisfyTwoOutOfSix)) why model categories satisfy 2-out-of-6. <a href="https://ncatlab.org/nlab/revision/diff/two-out-of-six+property/6">diff</a>, <a href="https://ncatlab.org/nlab/revision/two-out-of-six+property/6">v6</a>, <a href="https://ncatlab.org/nlab/show/two-out-of-six+property">current</a>

   Have made more explicit (now here) why model categories satisfy 2-out-of-6.

   diff, v6, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJul 24th 2023
   • (edited Jul 24th 2023)
   • PermaLink
   Author: Urs
   Format: MarkdownItexAdded ([here](https://ncatlab.org/nlab/show/two-out-of-six+property#When2OutOf6ImpliesTwoOutOfThree)) missing assumption (that identities need to be among the class of weak equivalence) to proof that 2-out of-6 implies 2-out-of-3. <a href="https://ncatlab.org/nlab/revision/diff/two-out-of-six+property/6">diff</a>, <a href="https://ncatlab.org/nlab/revision/two-out-of-six+property/6">v6</a>, <a href="https://ncatlab.org/nlab/show/two-out-of-six+property">current</a>

   Added (here) missing assumption (that identities need to be among the class of weak equivalence) to proof that 2-out of-6 implies 2-out-of-3.

   diff, v6, current