Is there a way to define perverse sheaves categorically/geometrically? Definitions like the following from lectures by Sophie Morel:



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> The category of perverse sheaves on $X$ is $\mathrm{Perv}(X,F):=D^{\leq 0} \cap D^{\geq 0}$. We write $^p\mathrm{H}^k \colon D\_c^b(X,F) \to \mathrm{Perv}(X,F)$ for the cohomology functors given by the $\mathrm{t}$-structure.
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are well and good, but to me, it feels like they come with too many "luggages", and therefore make me feel like I don't have as good of an intuition of derived categories as I should.



So what exactly are perverse sheaves anyway?
An $\infty$-categorical perspective is given here <https://arxiv.org/abs/1507.03913> and a triangulated expansion of those ideas is here <https://arxiv.org/abs/1806.00883>


More or less, perverse sheaves are the heart of a certain $t$-structure that you build "gluing along a perversity datum".


