Uploaded October 2021 | Updated September 2026, 2 weeks ago

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This lecture is part of an online course on rings and modules.

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.


For the other lectures in the course see youtube.com/playlist?list=PL8yHsr3EFj52XDLrmvrFDgwcf6XOm2TEE