Re: Sheaves and the empty set
- From: Jose Capco <cliomseerg@xxxxxxxxxxxxxxxxxxxxxxxxx>
- Date: 18 May 2007 14:36:28 -0700
On May 18, 2:15 pm, Jannick Asmus <jannick.n...@xxxxxx> wrote:
What if C is the category of rings with unity and ring homomorphisms
preserving unity?
Then the terminal object of this category is nothing but the zero
ring..
recall that the terminal object (-the- because terminal objects are
unique up to isomorphism) is the object B, by which for all A in my
category there is ONLY ONE morphism A->B
the zero ring satisfies this. Theres only one ring homomorphism R->{0}
and thats the one that takes every x in R to 0.. unity is preserved in
this homomorphism, becuase zero and one/unity are the same in the zero
ring (this only happens in the zero ring in the category of
commutative unitary rings). Some mathematicians "try" to define rings
in such a way that 0=/=1 but this does more harm than good imo, since
otherwise the commutative unitary rings won't be a complete category..
a terminal/initial object is sometimes very useful imo.
Sincerely,
Jose Capco
.
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- Sheaves and the empty set
- From: Jose Capco
- Re: Sheaves and the empty set
- From: Jannick Asmus
- Sheaves and the empty set
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