Contents

# Contents

## Idea

Pro-homotopy theory involves the study of model categories and other abstract homotopy theoretic structure on pro-categories of topological spaces or simplicial sets. (The term can also be used for any extension of homotopical structures for a category $C$ to the corresponding category $Pro(C)$ of pro-objects in $C$.)

## Uses

and is closely related to profinite homotopy theory.

The homotopy theory of simplicial profinite spaces has been explored by Fabien Morel and Gereon Quick.

For Morel’s theory see

• F. Morel, Ensembles profinis simpliciaux et interprétation géométrique du foncteur $T$, Bull. Soc. Math. France, 124, (1996), 347–373,

The initial reference to Quick’s work is :

• G. Quick, Profinite homotopy theory, PDF

but a correction to an error in the proof of the main result was included in

• G. Quick, Continuous group actions on profinite spaces, J. Pure Appl. Algebra 215 (2011), 1024-1039.

## References

For one of the earliest model structures, namely the strict model structure on $Pro(C)$, see

• D.A. Edwards and H. M. Hastings, (1976), Čech and Steenrod homotopy theories with applications to geometric topology, Lecture Notes in Maths. 542, Springer-Verlag, pdf

More recent contributions include:

Last revised on September 14, 2021 at 05:21:05. See the history of this page for a list of all contributions to it.