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hi Im Daniel Chan from human SW Sydney welcome to another adventure in pure mathematics in this video I want to talk about the very very important notion of three resolutions in homological algebra and one way to think about what this notion does for you is it collects all the syzygy information that we saw in help its sister Gs theorem okay so lets start with the first notion that we need to introduce that of exact sequences and one way to think about exact sequences is if youre not about complexes its a complex with no or trivial homology or Karim ology okay so lets go through the definition work in the setting of modules over sombering park and what were going to do is were going to look at a sequence of our modules MI my plus one my plus two and so forth its possibly infinite but maybe it stops somewhere okay so these are modules and in between you have are in your maps between them like that okay so the first thing to define is what it means to be a exact at one of these
