I'm an economist, not a mathematician. I've been trying to make sense of some concepts in functional analysis: dual, bidual, adjoint, natural mapping. The definitions of these notions come out of nowhere and I see no intuition. I thought that I should read category theory to see the big picture. ...

Category theory is famous for its founder's motto that "adjoints are everywhere". While the original context of his quote was meant to encompass mathematics, we have since seen the concept of adjoints, a.k.a. duality, a.k.a. isomorphisms, extend far beyond the realm of pure mathematics into areas...

Consider the abelian cyclic group of twelve elements, C12, with generators $$ C12^* = (e^1, e^5, e^7, e^{11}).$$ The cayley diagram generated by $e^1$ is a circle of twelve directed links for the twelve applications of the $e^1$ generator. Taking this as a small category, there must be an opp...

There's another possibility that hasn't been mentioned in the OP, and the one I would prefer: kill it! I don't see subspaces as a tag that will ever be consistently used, and not something that has a concrete enough meaning to allow for an easy delineation of when it should be used. Should you a...

If you think that the tags maximal-ideals and prime-ideals should be synonyms of ideals, upvote this answer.

I often want to improve the tags on questions like "Is it possible to make this expression shorter?". This question asks how to simplify or evaluate the finite sum $$ \sum_{i=1}^n\left( 2^{i-1} a_i \sum_{k=0}^{n-i}10^k \binom{n-i}{k} \right)$$ Questions of this type seem to be fairly common,...

The exponential function can be written as $$e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots.$$ The subspace of all polynomials is $$\text{span}\{1, x,x^2, \dots \}$$ Sure $e^x$ is in this set?