40 research outputs found
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