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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeFeb 2nd 2014
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   Author: Urs
   Format: MarkdownItexcreated _[[finite homotopy type]]_, just for completeness. This just a distraction when I saw that it was missing,while I was really going to create an entry on truncated homotopy types with finite homotopy groups. The main problem about them is that nobody agrees on how to call them ;-) In [[groupoid cardinality]] they have been called "tame", some call them $\pi$-finite,I suppose, and homological algebra suggests "of [[finite type]]", which in itself is good, however rather badly goes together with the crucially different "finite homotopy type".

   created finite homotopy type, just for completeness.

   This just a distraction when I saw that it was missing,while I was really going to create an entry on truncated homotopy types with finite homotopy groups.

   The main problem about them is that nobody agrees on how to call them ;-)

   In groupoid cardinality they have been called “tame”, some call them $\pi$-finite,I suppose, and homological algebra suggests “of finite type”, which in itself is good, however rather badly goes together with the crucially different “finite homotopy type”.

2. • CommentRowNumber2.
   • CommentAuthorTim_Porter
   • CommentTimeFeb 2nd 2014
   • (edited Feb 2nd 2014)
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   Author: Tim_Porter
   Format: MarkdownItexThe same sort of problem occurs with profinite homotopy types. This is complicated by the fact that simplicial profinite spcaes and pro-simplicial finite spaces, and pro-finite homotopy types all look to be almost the same ..... but the morphisms go all over the place. (There is a paper by Isaksen that discusses this, but it seems to have been controversial.) Urs: do you know the paper: G. J. Ellis, Spaces with finitely many non-trivial homotopy groups all of which are finite, Topology, 36, (1997), 501–504, ISSN 0040-9383. This might be relevant.

   The same sort of problem occurs with profinite homotopy types. This is complicated by the fact that simplicial profinite spcaes and pro-simplicial finite spaces, and pro-finite homotopy types all look to be almost the same ….. but the morphisms go all over the place. (There is a paper by Isaksen that discusses this, but it seems to have been controversial.)

   Urs: do you know the paper: G. J. Ellis, Spaces with finitely many non-trivial homotopy groups all of which are finite, Topology, 36, (1997), 501–504, ISSN 0040-9383.

   This might be relevant.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeFeb 2nd 2014
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   Author: Urs
   Format: MarkdownItexthanks for the reference. I have put it into a stub _[[homotopy type with finite homotopy groups]]_ for the moment. But that needs to be expanded. If you feel like adding a comment on how the terminology is even more of a mess for pro-theory, please feel invited.

   thanks for the reference. I have put it into a stub homotopy type with finite homotopy groups for the moment. But that needs to be expanded.

   If you feel like adding a comment on how the terminology is even more of a mess for pro-theory, please feel invited.

4. • CommentRowNumber4.
   • CommentAuthorTim_Porter
   • CommentTimeFeb 2nd 2014
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   Author: Tim_Porter
   Format: MarkdownItexI would have to sort out the mess to my own satisfaction first!!! :-( but I should do that.

   I would have to sort out the mess to my own satisfaction first!!! :-( but I should do that.