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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 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 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.
   • CommentAuthorzskoda
   • CommentTimeAug 30th 2024
   • PermaLink
   Author: zskoda
   Format: MarkdownItexAdded a bit, including the original reference by G. B. <a href="https://ncatlab.org/nlab/revision/diff/Birkhoff%27s+HSP+theorem/7">diff</a>, <a href="https://ncatlab.org/nlab/revision/Birkhoff%27s+HSP+theorem/7">v7</a>, <a href="https://ncatlab.org/nlab/show/Birkhoff%27s+HSP+theorem">current</a>

   Added a bit, including the original reference by G. B.

   diff, v7, current

2. • CommentRowNumber2.
   • CommentAuthornLab edit announcer
   • CommentTimeDec 29th 2024
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexupdate lk sheaf <a href="https://ncatlab.org/nlab/revision/diff/Birkhoff%27s+HSP+theorem/9">diff</a>, <a href="https://ncatlab.org/nlab/revision/Birkhoff%27s+HSP+theorem/9">v9</a>, <a href="https://ncatlab.org/nlab/show/Birkhoff%27s+HSP+theorem">current</a>

   update lk

   sheaf

   diff, v9, current

3. • CommentRowNumber3.
   • CommentAuthornLab edit announcer
   • CommentTimeApr 2nd 2025
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexCorrected definition of "closed under homomorphic image"; under the old definition, the condition would be redundant, because $im(\phi)$ is just a subalgebra of $B \in C$. Cecilia Knäbchen <a href="https://ncatlab.org/nlab/revision/diff/Birkhoff%27s+HSP+theorem/10">diff</a>, <a href="https://ncatlab.org/nlab/revision/Birkhoff%27s+HSP+theorem/10">v10</a>, <a href="https://ncatlab.org/nlab/show/Birkhoff%27s+HSP+theorem">current</a>

   Corrected definition of “closed under homomorphic image”; under the old definition, the condition would be redundant, because is just a subalgebra of .

   Cecilia Knäbchen

   diff, v10, current