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.