nLab
pro-homotopy theory

Idea

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 $C$ to the corresponding $\mathrm{Pro}(C)$.)

Uses

• In strong shape theory,

• In étale homotopy theory and motivic homotopy.

• In proper homotopy theory.

References

• D. C. Isaksen, A model structure on the category of pro-simplicial sets, Trans. Amer. Math. Soc., 353, (2001), 2805–2841.