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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJun 3rd 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexstarted an entry [[looping and delooping]] in an attempt to bring statements together in one place that are currently a bit scattered over the $n$Lab. Not done yet, but need to quit now.

   started an entry looping and delooping in an attempt to bring statements together in one place that are currently a bit scattered over the $n$Lab. Not done yet, but need to quit now.

2. • CommentRowNumber2.
   • CommentAuthorjim_stasheff
   • CommentTimeJun 6th 2011
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   Author: jim_stasheff
   Format: TextTried to edit don't know if it worked

   Tried to edit
   don't know if it worked
3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJun 6th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexHi Jim, yes, your edits did work. You asked in the Idea-section which definition of loops and which definition of delooping is meant. But the idea is that in the "Idea"-section I don't want to specify technical details, but just ideas ;-) To hopefully make this clearer, I have added the following sentence > What all these terms ("loops" $\Omega$, "delooping" $B$ etc.) mean in detail and how they are _presented_ concretely depends on the given setup. We discuss some of these below in the section _Examples_ . Is that better?

   Hi Jim,

   yes, your edits did work.

   You asked in the Idea-section which definition of loops and which definition of delooping is meant. But the idea is that in the “Idea”-section I don’t want to specify technical details, but just ideas ;-)

   To hopefully make this clearer, I have added the following sentence

   What all these terms (“loops” $\Omega$, “delooping” $B$ etc.) mean in detail and how they are presented concretely depends on the given setup. We discuss some of these below in the section Examples .

   Is that better?

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJul 21st 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have slightly polished and expanded at [[looping and delooping]] the part about "in parameterized $\infty$-groupoids"

   I have slightly polished and expanded at looping and delooping the part about “in parameterized $\infty$-groupoids”

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeApr 16th 2015
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added ([here](http://ncatlab.org/nlab/show/looping#ForPlainGroupsDeloopingToGroupoids)) an exposition which spells out in detail the equivalence $$ Grp \stackrel{\underoverset{\simeq}{\pi_1 = \Omega_\ast}{\longleftarrow}}{\underset{\mathbf{B}}{\longrightarrow}} Grpd^{\ast/}_{\geq 1} $$ As usual there are choices to be made in the notation as to whether $\mathbf{B}G$ has composition given by multiplication from the left or from the right, and whether $Ad_h$ is $h^{-1} (-)h$ or the other way around, and one tends to end up wondering which combination of conventions leads to a minimum of $(-)^{-1}$-symbols. I don't claim that I got that minimum, but I want to leave it as is for the moment.

   I have added (here) an exposition which spells out in detail the equivalence

   $$Grp \stackrel{\underoverset{\simeq}{\pi_1 = \Omega_\ast}{\longleftarrow}}{\underset{\mathbf{B}}{\longrightarrow}} Grpd^{\ast/}_{\geq 1}$$

   As usual there are choices to be made in the notation as to whether $\mathbf{B}G$ has composition given by multiplication from the left or from the right, and whether $Ad_h$ is $h^{-1} (-)h$ or the other way around, and one tends to end up wondering which combination of conventions leads to a minimum of $(-)^{-1}$-symbols. I don’t claim that I got that minimum, but I want to leave it as is for the moment.

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeApr 16th 2015
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have also copied this over to _[[geometry of physics -- groups]]_, where I'll be adding some more glue to it.

   I have also copied this over to geometry of physics – groups, where I’ll be adding some more glue to it.