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Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.
11
votes
Accepted
About higher Ext in R-Mod
They correspond to longer exact sequences under an equivalence relation due to Yoneda. See chapter III.3 (p. 82ff) of MacLane's Homology (or briefly on the wikipedia page for the Ext functor). There …
11
votes
Abstract nonsense versions of "combinatorial" group theory questions
Sylow subgroups are an example of a type of object satisfying a sort of universal property. Exploring other objects with similar properties gave birth to the modern theory of finite soluble groups in …
87
votes
Accepted
Why is there no Cayley's Theorem for rings?
Every (associative, unital) ring is a subring of the endomorphism ring of its underlying additive group. Rings act on abelian groups; groups act on sets. The universal action on an abelian group is …
11
votes
Accepted
Why did people originally like Frobenius algebras?
Frobenius's original turn-of-the-century perspective was the nonvanishing of a determinant. Brauer–Nesbitt–Nakayama studied some equivalent definitions in the late 30s and early 40s. For instance, an …