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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.
   • CommentAuthorUrs
   • CommentTimeDec 4th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexjust for completeness, to go along with _[[cyclic group]]_ etc. <a href="https://ncatlab.org/nlab/revision/Q%2FZ/1">v1</a>, <a href="https://ncatlab.org/nlab/show/Q%2FZ">current</a>

   just for completeness, to go along with cyclic group etc.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorTodd_Trimble
   • CommentTimeDec 18th 2020
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexAdded more material: $\mathbb{Q}/\mathbb{Z}$ as a filtered colimit of finite cyclic groups, as a coproduct of Prüfer groups, and as an injective cogenerator. <a href="https://ncatlab.org/nlab/revision/diff/Q%2FZ/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/Q%2FZ/2">v2</a>, <a href="https://ncatlab.org/nlab/show/Q%2FZ">current</a>

   Added more material: $\mathbb{Q}/\mathbb{Z}$ as a filtered colimit of finite cyclic groups, as a coproduct of Prüfer groups, and as an injective cogenerator.

   diff, v2, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeDec 18th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks! I have given the paragraph on Prüfer groups its own sub-subsection header, and have renamed the sub-subsection "Properties" to "Further properties, to avoid the repetition. Also, I have added hyperlinks to a few more technical terms (such as _[[Ab]]_) and added cross-links from other entries (such as [[Prüfer group]], [[root of unity]]) to this entry here. <a href="https://ncatlab.org/nlab/revision/diff/Q%2FZ/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/Q%2FZ/3">v3</a>, <a href="https://ncatlab.org/nlab/show/Q%2FZ">current</a>

   Thanks!

   I have given the paragraph on Prüfer groups its own sub-subsection header, and have renamed the sub-subsection “Properties” to “Further properties, to avoid the repetition.

   Also, I have added hyperlinks to a few more technical terms (such as Ab) and added cross-links from other entries (such as Prüfer group, root of unity) to this entry here.

   diff, v3, current

4. • CommentRowNumber4.
   • CommentAuthorDavid_Corfield
   • CommentTimeDec 18th 2020
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexNothing intelligent to say, but is there a way to link this page to [[Brown-Comenetz duality]]?

   Nothing intelligent to say, but is there a way to link this page to Brown-Comenetz duality?

5. • CommentRowNumber5.
   • CommentAuthorTodd_Trimble
   • CommentTimeDec 18th 2020
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexDavid, I don't see why not, but looking at [[Brown-Comenetz duality]], I see it described as a Pontrjagin dual, which is probably not a good idea without some qualifier, e.g., "algebraic Pontrjagin" dual or something. Any ideas?

   David, I don’t see why not, but looking at Brown-Comenetz duality, I see it described as a Pontrjagin dual, which is probably not a good idea without some qualifier, e.g., “algebraic Pontrjagin” dual or something. Any ideas?