Freyd - Mitchell is installing theorem
Freyd-Mitchell's embedding theorem states that : if A is a tiny abelian group, after that there exists a ring R and also a complete, loyal and also specific functor F : A → R - Mod.
This is fairly the theory and also has numerous valuable applications (it permits one to do layout chasing in abstract abelian groups, etc)
I have actually been asked to state and also confirm the theory in class (a homological algebra training course). Nonetheless, by reviewing the messages I was advised, I'm concerning to give up :
Freyd is Abelian Categories claims that the message, excepting the workouts, attempts to be a geodesic bring about the theory. If you obtain the workouts, possibly the message is 120 web pages long. Difficult to do in 2 :30 hrs. To offer you a suggestion, the training course I'm taking is based in Rotman is "An Introduction to Homological Algebra" which operates in R - Mod ...
Mitchell is Theory of Categories is really tough to read, as well as additionally to confirm the theory you have lots of interpretations and also suggestions and also lemmas to confirm.
Weibel is An Introduction to Homological Algebra reroutes me to Swan, The Theory of Sheaves, a publication which is inaccessible in my college is collection. I've scanned Swan is Algebraic K - Theory : the theory is confirmed, yet it is additionally long, tough and also excruciating to read, and also thinks a great deal of expertise I do not have (I had actually never ever seen a weakly effaceable functor, or a Serre subcategory ; and also it absolutely is not popular to me that the group of additive functors from a tiny abelian group to the group of abelian teams is well - powered, appropriate full, and also has injective envelopes!)
I'm beginning to think it is a difficult job. Yet possibly there are extra modern-day evidence which call for much less hefty equipment and also trivialities?