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Jun
22 |
awarded | Autobiographer |
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 |