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Apr
27
awarded  Yearling
Apr
10
comment Are product / coproduct projections / inclusions 'semistrict'?
$\mathbf{Grp}$ is perhaps the most natural nonadditive category I had in mind.
Apr
10
asked Are product / coproduct projections / inclusions 'semistrict'?
Apr
6
accepted Composition of stable-pseudomonomorphisms
Apr
5
answered Composition of stable-pseudomonomorphisms
Apr
4
asked Composition of stable-pseudomonomorphisms
Mar
29
comment Sufficient conditions for the category of group objects to have coproducts
Finally, if I understand you correctly, then $\mathbf{C}$ cocomplete, cartesian closed, and locally presentable is sufficient to guarantee that the category of group objects is cocomplete?
Mar
29
comment Sufficient conditions for the category of group objects to have coproducts
Perhaps I could verify the other conditions of Beck's Theorem by hand, but I don't know enough category theory to make their deduction "automatic". What fact tells us immediately these conditions are satisfied without having to check?
Mar
29
comment Sufficient conditions for the category of group objects to have coproducts
I have a couple of follow-up questions about this, which for convenience and reasons of size, I will break-up into separate comments. Actually one of the things I got stuck on last night was the application of the (general) adjoint functor theorem to the forgetful functor, in particular, the verification of the solution set condition. It seems that for $\mathbf{C}$ a general cocomplete category, this is hopeless (though I didn't bother looking for a counter-example)? What are sufficient conditions to make this work?
Mar
29
asked Sufficient conditions for the category of group objects to have coproducts
Mar
23
revised Image factorisation in pointed categories
Fixed typo
Feb
24
awarded  Popular Question
Feb
19
awarded  Famous Question
Jan
29
revised Interesting sites without pull-backs
added 409 characters in body
Jan
29
comment Interesting sites without pull-backs
"Also, you don't need pullbacks in order to use the usual definition of a sheaf: it suffices to show that pullbacks (i.e., base changes) of covering families exists and are covering families. " ---- That's a good point. This is what I actually had in mind when writing the question, though I carelessly stated it in terms of the category itself having pull-backs. I will edit the question accordingly.
Jan
27
asked Interesting sites without pull-backs
Dec
29
accepted Under what conditions is the exponential map on a Lie algebra injective?
Dec
3
accepted Mathematical significance of the “Dirac conjugate”
Nov
8
answered Compactification: density of a uniform space $X$ in the spectrum of $UC^b(X)$
Oct
24
awarded  Notable Question