9 citations · 15 across the 6 of their papers we have counts for
5 papers · 1 filter
Hypercovers in topology
Daniel Dugger, Daniel C. Isaksen
We show that if U is a hypercover of a topological space X then the natural map from hocolim U to X is a weak equivalence. This fact is used to construct topological realization fu…
Strict model structures for pro-categories
Daniel C. Isaksen
We show that C if is a proper model category, then the pro-category pro-C has a strict model structure in which the weak equivalences are the levelwise weak equivalences. The stric…
A model structure on the category of pro-simplicial sets
Daniel C. Isaksen
We study the category pro-SSet of pro-simplicial sets, which arises in etale homotopy theory, shape theory, and pro-finite completion. We establish a model structure on pro-SSet so…
Calculating limits and colimits in pro-categories
Daniel C. Isaksen
We present some constructions of limits and colimits in pro-categories. These are critical tools in several applications. In particular, certain technical arguments concerning stri…
Etale realization on the A^1-homotopy theory of schemes
Daniel C. Isaksen
We compare Friedlander's definition of the etale topological type for simplicial schemes to another definition involving realizations of pro-simplicial sets. This can be expressed…