  Bordered Floer homology assigns invariants to 3-manifolds with boundary, such
that the Heegaard Floer homology of a closed 3-manifold, split into two pieces,
can be recovered as a tensor product of the bordered invariants of the pieces.
We construct cornered Floer homology invariants of 3-manifolds with
codimension-2 corners, and prove that the bordered Floer homology of a
3-manifold with boundary, split into two pieces with corners, can be recovered
as a tensor product of the cornered invariants of the pieces.
