We define categorical matrix factorizations in a suspended additive category,
with respect to a central element. Such a factorization is a sequence of maps
which is two-periodic up to suspension, and whose composition equals the
corresponding coordinate map of the central element. When the category in
question is that of free modules over a commutative ring, together with the
identity suspension, then these factorizations are just the classical matrix
factorizations. We show that the homotopy category of categorical matrix
factorizations is triangulated, and discuss some possible future directions.
This is joint work with Dave Jorgensen.
- Algebra Seminar