A new model for pro-categories

In this paper we present a new way to construct the pro-category of a category. This new model is very convenient to work with in certain situations. We present a few applications of this new model, the most important of which solves an open problem of Isaksen [Isa] concerning the existence of functorial factorizations in what is known as the strict model structure on a pro-category. Additionally we explain and correct an error in one of the standard references on pro-categories.Comment: Substantial overlap with arXiv:1305.4607. Accepted for publication in the Journal of Pure and Applied Algebra, reference: JPAA-504

Contractibility of the Space of Opers for Classical Groups

The geometric Langlands program is an exciting direction of research, although a lot of progress has been made there are still open questions and gaps. One of the necessary steps for this program is the proof of the existence and the cohomological triviality (more precisely, the O- contractibility) of the space of rational opers. In this paper, we prove the homotopical contractibility of the space of rational opers for classical groups