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A question in Tennison's Sheaf Theory is about the category of pointed sets and its characteristics. I have that

  • its zero object is given by $(\{x\},x)$
  • the kernel of $f\colon (A,a)\to (B,b)$ is given by $(f^{-1}(b),a)$
  • the cokernel is given by $(f(A),b)$
  • epimorphisms are surjective maps

but I fail to see why this breaks down cokernels.

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    @wxu: You're right, and that was why I couldn't see the obvious. As @beroal mentioned, the surjectivity fails in the case of split epimorphisms. Thanks for the answers!2011-06-19

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