In [2] Baez and Dolan established their stabilization hypothesis as one of a list of the key properties that a good theory of higher categories should have. It is the analogue for n-categories of the well-known stabilization theorems in homotopy theory. To explain the statement, recall that Baez-Dolan introduce the notion of k-uply monoidal n-category which is an n+ k-category having only one i...

Abstract Cartesian reverse differential categories (CRDCs) are a recently defined structure which categorically model the differentiation operations used in supervised learning. Here, we define related called monoidal category , prove important results about its relationship to CRDCs, and provide examples of both structures, including coming from models quantum computation.

We prove the Existential Closedness conjecture for differential equation of j j -function and its derivatives. It states that in a differentia...