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