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Topic: Can Hom(A,B) be Empty in a Category?
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Posts: 28
From: NYC
Registered: 12/8/12
Can Hom(A,B) be Empty in a Category?
Posted: Dec 8, 2012 8:11 AM
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Hi, All:

I am trying to see if I can define a category in which the morphisms are quotients of topolocal spaces. I don't have any special condition for choosing the objects.

Do I need to define the objects to be an ordered nested sequence ( by inclusion ) of spaces , so that, say if i<j
then Xi<Xj and the quotient Xj/Xi is defined , or can I just have Hom(A,B)={ } when neither A or B are a subspace of the other?

Thanks in Advance.

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