We introduce the concept of a morphism from the set of Butson Hadamard matrices over k th roots of unity to the set of Butson matrices over l roots of unity. As concrete examples of such morphisms, we describe tensor-product-like maps which reduce the order of the roots of unity appearing in a Butson matrix at the cost of increasing the dimension. Such maps can be constructed from Butson matric...

In this paper, we will give a natural definition for morphisms between multiplicative unitaries. We will then discuss some equivalences of this definition and some interesting properties of them. Moreover, we will define normal sub-multiplicative unitaries for multiplicative unitaries of discrete type and prove an imprimitivity type theorem for discrete multiplicative unitaries.

Given an arbitrary locally finitely presentable category K and finitary monads T and S on K , we characterize monad morphisms α : S −→ T with the property that the induced functor α∗ : K T −→ K S between the categories of Eilenberg-Moore algebras is fully faithful. We call such monad morphisms dense and give a characterization of them in the spirit of Beth’s definability theorem: α is a dense m...

We develop a general setting for the treatment of extensions of categories by means of freely adjoined morphisms. To this end, we study what we call composition graphs, i.e. large graphs with a partial binary operation on which we impose only rudimentary requirements. The quasicategory thus obtained contains the quasicategory of all categories as a full reflective subquasicategory; we character...

We study the stability of harmonic morphisms as a subclass of harmonic maps. As a general result we show that any harmonic morphism to a manifold of dimension at least three is stable with respect to some Riemannian metric on the target. Furthermore we link the index and nullity of the composition of harmonic morphisms with the index and nullity of the composed maps.

We present an approach to modeling computational calculi using higher category theory. Specifically we present a fully abstract semantics for the π-calculus. The interpretation is consistent with Curry-Howard, interpreting terms as typed morphisms, while simultaneously providing an explicit interpretation of the rewrite rules of standard operational presentations as 2-morphisms. One of the key ...