Let $X$ be a nice enough topological space, perhaps a complex algebraic variety with its analytic topology. I'm hoping someone could help me prove that the category $\text{Constr}(X)$ of constructible sheaves on $X$ is abelian. 


I think one could use that subsheaves and quotients of local systems are local systems. However, conceptually what is confusing me is that given two constructible sheaves $\mathcal{F}, \mathcal{G}$, they might be constructible with respect to completely different Whitney stratifications of X, right? 


So given a morphism $\mathcal{F} \to \mathcal{G}$ of constructible sheaves, can you always "refine" the two Whitney stratifications to get one such that the morphism restricts to a morphism of local systems? 


Or should I be thinking along another lines? 



Prove category of constructible sheaves is abelian
[Verdier has proved](https://eudml.org/doc/142424) (for multiple classes of spaces, including in particular complex varieties) that for any finite set of analytic subsets, there exists a Whitney stratification for which all these analytic subsets are unions of strata.


In particular, given two constructible sheaves, and a stratification on which they are lisse, there exists a Whitney stratification that refines both of them. 


This suffices to check that kernels and cokernels of maps of constructible sheaves are constructible, as well as direct sums of constructible sheaves.


