stacks/stacks-project — pull request #3 by dbergh (2013-09-23 09:10:03+00:00)
Title: New proof of Lemma 0032

I wrote down a new proof for the lemma about colimits indexed filtered categories as colimits indexed by partially ordered sets. The proof is maybe slightly too long. It could be shortened by doing any of these things:

1. Split the Lemma in two. One which asserts the existence of a cofinal functor I_0 -> I and corollary using a formulation in terms of systems.
2. The definition of cone and cocone could be moved to the section about limits (002D)
3. The definition of finiely generated category could be moved to the section about finite limits a colimits (04AS)
4. The fact that any finite (finitely generated) diagram in a filtered category could be stated as a separate lemma in the section about filtered categories (04AX).
5. The statement that a product of filtered categories is filtered could be stated as a separate lemma.
6. The statement that compositions of cofinial functors are cofinal could be stated as a separate lemma.