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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
   • CommentTimeMay 14th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexstub for _[[uniformly hyperfinite algebra]]_

   stub for uniformly hyperfinite algebra

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeMay 17th 2012
   • PermaLink
   Author: zskoda
   Format: MarkdownItexColimit may be indexed over any directed set here, not just a sequence ?

   Colimit may be indexed over any directed set here, not just a sequence ?

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMay 17th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexTrue, the literature speaks of sequential colimits. Does it make a difference?

   True, the literature speaks of sequential colimits. Does it make a difference?

4. • CommentRowNumber4.
   • CommentAuthorzskoda
   • CommentTimeMay 17th 2012
   • PermaLink
   Author: zskoda
   Format: MarkdownItexI think it should be important. Namely, it is supposed to be one of the major techniques to look at shape theory in noncommutative generalization (see e.g. papers by Dadarlat). In the commutative case, in shape theory, one approximates with inverse systems (not just sequences) of ANRs. I forgot which class of $C^\ast$-algebras they exactly corresponds in commutative case (there is a paper which does this). But I am rusty in this, I recall listening a comprehensive talk in Spring 2002 at Purdue by some collaborator of Dadarlat, this talk spurred my interest in UHF algebras and then I looked again few times few years ago. But now my memory is rusty. In any case, I think it deserves some care eventually. Hopefully I will have once a chance to work more at the entry and literature.

   I think it should be important. Namely, it is supposed to be one of the major techniques to look at shape theory in noncommutative generalization (see e.g. papers by Dadarlat). In the commutative case, in shape theory, one approximates with inverse systems (not just sequences) of ANRs. I forgot which class of $C^\ast$-algebras they exactly corresponds in commutative case (there is a paper which does this). But I am rusty in this, I recall listening a comprehensive talk in Spring 2002 at Purdue by some collaborator of Dadarlat, this talk spurred my interest in UHF algebras and then I looked again few times few years ago. But now my memory is rusty. In any case, I think it deserves some care eventually. Hopefully I will have once a chance to work more at the entry and literature.