Category Theory Vs. Abstract Algebra
Here's the dirt on how these objects relate to one another:
All the major classes of structures in abstract algebra are examples of categories: the category of groups, the category of abelian groups, the category of rings, and so on.
At a more advanced level, many algebraic constructions are best defined by use of "universal diagrams", which notion is inherently categorical. See, for example, the abstract definition of the tensor product or even the direct product.
At a more advanced level, many algebraic constructions are best defined by use of "universal diagrams", which notion is inherently categorical. See, for example, the abstract definition of the tensor product or even the direct product.