/sci/ - Science & Math

>>9245590
>existence
>nonconstructively
I think you mean "non-refutation of existence" there.

>>9245847
>the cartesian product of nonempty sets may be empty
Literal retard and or freshman detected, kill yourself. I wouldn't be surprised if you think that because excluded middle isn't provable constructively, there are somehow propositions in constructive foundations which are neither true, nor false.

>>9026508
2. is easy, assuming we know the following things:
>module categories satisfy two topos axioms but not necessarily the subobject classifier thingy (lawvere-tierney)
>in a topos an arrow whose codomain is an initial object is an isomorphism
>trivial modules are both initial and terminal
>there are non-trivial modules over unitary rings
It follows that there can be no subobject classifiers for these module categories, in particular the category of abelian groups.