I'm familiar with topology and category theory a little bit as well as inverse limits of inverse systems. I would like to understand the shape group better.
For example, one could describe the fundamental group as "mapping in loops modulo homotopy". What are the elements of the shape group? Are the elements equivalence classes of maps modulo some relation? Basically, I would like to know what the definition of the elements of the shape group is.
Can anyone help me out please? I'd be so grateful!
Typing 'Shape Group' into the search field of MathSciNet yields numerous paper on the subject. For instance:
Brazas, Jeremy(1-GAS-MS); Fabel, Paul(1-MSS) Thick Spanier groups and the first shape group. Rocky Mountain J. Math. 44 (2014), no. 5, 1415–1444. 55Q05 (55Q07 57M05)
Fischer, Hanspeter(1-BLS); Zastrow, Andreas(PL-GDAN) Generalized universal covering spaces and the shape group. Fund. Math. 197 (2007), 167–196.
And here is the first paper (chronologically) on MathSciNet which has the term 'shape group' in the title.
Sanders, Thomas J. Shape groups for Hausdorff spaces. Glasnik Mat. Ser. III 8(28) (1973), 297–304. (Reviewer: S. Mardesic)