Example 12.3.13. Let k be a field. Consider the category of filtered vector spaces over k. (See Definition 12.19.1.) Consider the filtered vector spaces (V, F) and (W, F) with V = W = k and
The map f : V \to W corresponding to \text{id}_ k on the underlying vector spaces has trivial kernel and cokernel but is not an isomorphism. Note also that \mathop{\mathrm{Coim}}(f) = V and \mathop{\mathrm{Im}}(f) = W. This means that the category of filtered vector spaces over k is not abelian.
Comments (2)
Comment #7840 by Zhenhua Wu on
Comment #8064 by Stacks Project on
There are also: