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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 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 internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure 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 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.
   • CommentAuthorporton
   • CommentTimeDec 23rd 2014
   • (edited Dec 23rd 2014)
   • PermaLink
   Author: porton
   Format: MarkdownItexIt seems that I've proved that every atomistic poset is a co-brouwerian lattice. The proof is an easy generalization of my theorem 6.86 in my draft book: [My book draft](http://www.mathematics21.org/binaries/volume-1.pdf) Is it true? (in other words, there is no error in my proof?) Please confirm the correctness of my result before we edit and include this result into [nLab article](http://nlab.mathforge.org/nlab/show/atom) Should we also edit [Wikipedia](https://en.wikipedia.org/wiki/Atom_%28order_theory%29) to include this fact? (If yes, which reference to cite?)

   It seems that I’ve proved that every atomistic poset is a co-brouwerian lattice.

   The proof is an easy generalization of my theorem 6.86 in my draft book:

   My book draft

   Is it true? (in other words, there is no error in my proof?)

   Please confirm the correctness of my result before we edit and include this result into nLab article

   Should we also edit Wikipedia to include this fact? (If yes, which reference to cite?)

2. • CommentRowNumber2.
   • CommentAuthorTodd_Trimble
   • CommentTimeDec 23rd 2014
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexIt's not true. For example, a typical [geometric lattice](http://en.wikipedia.org/wiki/Geometric_lattice) such as the lattice of equivalence relations on a finite set is not even distributive, much less co-brouwerian (meaning, I presume, opposite to a Heyting algebra).

   It’s not true. For example, a typical geometric lattice such as the lattice of equivalence relations on a finite set is not even distributive, much less co-brouwerian (meaning, I presume, opposite to a Heyting algebra).

3. • CommentRowNumber3.
   • CommentAuthorporton
   • CommentTimeDec 23rd 2014
   • PermaLink
   Author: porton
   Format: MarkdownItexOh, I see. My proof uses features specific to funcoids and does not generalize for other atomistic lattices. Sorry for your time spend about a non-existent generalization of my proof. (The proof itself is correct, just it cannot be generalized.)

   Oh, I see. My proof uses features specific to funcoids and does not generalize for other atomistic lattices.

   Sorry for your time spend about a non-existent generalization of my proof. (The proof itself is correct, just it cannot be generalized.)