We construct a supercategory that can be seen as a skew version of (thickened) KLR algebras
for the type
quiver. We use our supercategory to construct homological invariants of tangles and
show that for every link our invariant gives a link homology theory supercategorifying
the Jones polynomial. Our homology is distinct from even Khovanov homology and
we present evidence supporting the conjecture that it is isomorphic to odd Khovanov
homology. We also show that cyclotomic quotients of our supercategory give
supercategorifications of irreducible finite-dimensional representations of
of
level 2.
