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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeApr 3rd 2013
   • PermaLink
   Author: Urs
   Format: MarkdownItexdropped some lines into a new Properties-section in the old and neglected entry _[[bibundle]]_. But not for public consumption yet.

   dropped some lines into a new Properties-section in the old and neglected entry bibundle. But not for public consumption yet.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeApr 3rd 2013
   • (edited Apr 3rd 2013)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have now added a fair bit of content to _[[bibundle]]_. Firstly there is now what I think is a decent [Idea-section](http://ncatlab.org/nlab/show/bibundle#Idea) that lists the historical [References](http://ncatlab.org/nlab/show/bibundle#References) of which I have added a bunch. Then I worked on filling content into the section _[Properties -- Lie groupoid bibundles and Morita morphisms](http://ncatlab.org/nlab/show/bibundle#LieGroupoidBibundlesAndMoritaMorphisms)_. Currently what is there is a description of how to naturally extract a bibundle from a Morita morphism. I give the discussion in full generally for [[groupoid-principal infinity-bundles]] in an $\infty$-topos and in parallel spell out in components what it comes down to for the case of Lie groupoids. More can be done here. But at least it's a start, I think.

   I have now added a fair bit of content to bibundle.

   Firstly there is now what I think is a decent Idea-section that lists the historical References of which I have added a bunch.

   Then I worked on filling content into the section Properties – Lie groupoid bibundles and Morita morphisms.

   Currently what is there is a description of how to naturally extract a bibundle from a Morita morphism. I give the discussion in full generally for groupoid-principal infinity-bundles in an $\infty$-topos and in parallel spell out in components what it comes down to for the case of Lie groupoids.

   More can be done here. But at least it’s a start, I think.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeApr 5th 2013
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   Author: Urs
   Format: MarkdownItexadded a section _[Relation to groupoid convolution bimodules](http://ncatlab.org/nlab/show/bibundle#RelationToGroupoidConvolutionBimodules)_ which describes how to get from a groupoid bibundle a Hilbert $C^\ast$-bimodule over the corresponding groupoid convolution algebras, as described by Klaas Landsman. Needs another go of proof-reading, and a further comment on the $C^\ast$-completion is still missing. But I have to run now.

   added a section Relation to groupoid convolution bimodules which describes how to get from a groupoid bibundle a Hilbert $C^\ast$-bimodule over the corresponding groupoid convolution algebras, as described by Klaas Landsman.

   Needs another go of proof-reading, and a further comment on the $C^\ast$-completion is still missing. But I have to run now.