The previous lecture in this series is here. The next lecture in this series is here.
We discuss the problem of when a colimit of exact sequences is exact. We show that the colimit of exact sequences is at least right exact, but give an example to show that it is not always left exact. We find some conditions under which it is exact, such as direct sums, colimits over directed posets, and colimits over filtered categories.
This video is part of a lecture course by Richard Borcherds from 2021.