Intersection homological algebra
Mark Hovey
We investigate the abelian category which is the target of
intersection homology. Recall that, given a stratified space $X$, we
get intersection homology groups $I^{\perversity{p}}H_{n}X$ depending
on the choice of an $n$-perversity $\perversity{p}$. The
$n$-perversities form a lattice, and we can think of $IH_{n}X$ as a
functor from this lattice to abelian groups, or more generally
$R$-modules. Such perverse $R$-modules form a closed symmetric
monoidal abelian category. We study this category and its associated
homological algebra.