Pro-homotopy theory involves the study of model category and other abstract homotopy theoretic structure on pro-categories of spaces or simplicial sets. (The term can also be used for any extension of homotopical structures for a category to the corresponding .)
and is closely related to profinite homotopy theory.
For Morel’s theory see
A reference to Quick’s work is in
but a correction to an error in the proof of the main result was included in
For one of the earliest model structures, namely the strict model structure on , see
More recent contributions include:
D. C. Isaksen, A model structure on the category of pro-simplicial sets, Trans. Amer. Math. Soc., 353, (2001), 2805–2841.
D. C. Isaksen, Calculating limits and colimits in pro-categories, Fundamenta Mathematicae, 175, (2002), 175 – 194.
D. C. Isaksen, 2004, Strict model structures for pro-categories , in Categorical decomposition techniques in algebraic topology (Isle of Skye, 2001) , volume 215 of Progr. Math., 179 – 198, Birkhauser, Basel.
D. C. Isaksen, Completions of pro-spaces , Math. Z., 250, (2005), 113 – 143.