Hochschild-Mitchell homology HH∗(C) of a linear category C is one of some fundamental invariants of linear categories. A stratified linear category is a linear category C equipped with a distinguished linear subcategory C0 and a filtration on the set of objects such that the Hom spaces satisfy a certain factorization property. Then HH∗(C) is isomorphic to HH∗(C0). A similar result holds for cyclic homology as well. One can apply this result to the categorified quantum sl(2), for which we computed the HH0 in a joint work with Beliakova, Lauda, and Zivkovic. I plan to explain some other examples as well.