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Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.
2
votes
0
answers
192
views
Right adjoint completions
Forgive me if this question is not well thought out. I don't know how else to ask it.
The nlab page on completion gives some examples of completions which are left adjoints. These completions are "fr …
7
votes
0
answers
399
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Applications of Monadicity theorems
This is crosspost of this MSE question.
Having carefully read the proof of Beck's monadicity theorems and some related variations, I'm now hungry for cool applications.
For instance, I found these …
2
votes
0
answers
512
views
Neat applications of Galois descent?
I'm enjoying reading about Janelidze's categorical Galois theory, which gives as a special case the usual theorems of Galois descent (along torsors). The approach I took was just with covering space t …
41
votes
4
answers
6k
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Linear algebra in terms of abstract nonsense?
The categories of vector spaces and finite dimensional vector spaces are pretty much as nice as can be, I think.
I was wondering what portions of basic linear algebra (first couple of courses) fall o …