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seen Mar 8 at 12:18

Feb
6
awarded  Citizen Patrol
Feb
6
awarded  Yearling
Dec
13
awarded  Notable Question
Apr
11
awarded  Popular Question
Jan
17
comment Mathematical “urban legends”
I was once told about a philosophy essay that started "In this essay I will argue that the mind is identical to the brain, but not the other way around".
Jul
21
comment Is monomorphism going in both directions sufficient for isomorphism?
OK. But in general it is not true that subobjecthood determines and antisymmetric relation? But in most cases of interest, it will...
Jul
18
comment Is monomorphism going in both directions sufficient for isomorphism?
Right, so the problem is more that I'm misunderstanding what sort of work the categorical subobject idea is doing. But I'm glad I was right about monomorphisms...
Jul
18
awarded  Commentator
Jul
18
comment Is monomorphism going in both directions sufficient for isomorphism?
Here's the worry: in the two object category I defined above, each of A and B is a subobject of the other, but they are not isomorphic. Is this just a case where the categorical notion of "subobject" doesn't make sense, or have I misunderstood?
Jul
18
comment Is monomorphism going in both directions sufficient for isomorphism?
I don't know what you mean by "the morphisms ... over X are uniquely determined"
Jul
18
accepted Existence of convergent subsequences for all values in range?
Jul
18
comment Is monomorphism going in both directions sufficient for isomorphism?
So to get this straight: the definition of subobject requires that the monomorphism be unique?
Jul
18
comment Is monomorphism going in both directions sufficient for isomorphism?
The comment about subobjects is this. The definition of a subobject of an object A is: an object B with a monomorphism from B to A. So in my example, A is a subobject of B and B a subobject of A, but they aren't isomorphic. This seems weird, right?
Jul
18
asked Is monomorphism going in both directions sufficient for isomorphism?
Jul
15
comment Can a mathematical definition be wrong?
The first appendix to Proofs and Refutations contains another example: definitions of continuity.
May
5
answered Set theory for category theory beginners
Apr
29
accepted How would one extend the Brier score to an infinite number of forecasts?
Apr
28
asked How would one extend the Brier score to an infinite number of forecasts?
Mar
21
comment Is there a theorem that says that there is always more than one way to “continue a finite sequence”?
Nice characterisation of a similar point here: qntm.org/1111
Mar
15
comment Existence of convergent subsequences for all values in range?
Yes, I meant properties "like" mixing and ergodic. Sequences with the property I'm talking about seem to "bounce all over the place forever" in much the same way mixing functions do...