  We categorify a coideal subalgebra of the quantum group of
$\mathfrak{sl}_{2r+1}$ by introducing a $2$-category \`a la
Khovanov-Lauda-Rouquier, and show that self-dual indecomposable $1$-morphisms
categorify the canonical basis of this algebra. This allows us to define a
categorical action of this coideal algebra on the categories of modules over
cohomology rings of partial flag varieties and on the BGG category
$\mathcal{O}$ of type B/C.
