We determine the existential completion of a primary doctrine, and we prove that the 2-
monad obtained from it is lax-idempotent, and that the 2-category of existential doctrines is …

We construct a modular functor which takes its values in the monoidal bicategory of finite
categories, left exact functors and natural transformations. The modular functor is defined on …

Presheaves on a small category are well-known to correspond via a category of elements
construction to ordinary discrete fibrations over that same small category. Work of R. Par\'e …

Just as binary relations between sets may be understood as jointly monic spans, so too may
equivalence relations on the disjoint union of sets be understood as jointly epic cospans …

At the heart of differential geometry is the construction of the tangent bundle of a manifold.
There are various abstractions of this construction, and of particular interest here is that of …

A Q-system is a unitary version of a separable Frobenius algebra object in a C*-tensor
category. In a recent joint work with P. Das, S. Ghosh and C. Jones, the author has …

In this paper we consider the conditions that need to be satisfied by two families of
pseudofunctors with a common codomain for them to be collated into a bifunctor. We …

We introduce a candidate for the inner hom for $ Dbl^{st} _ {lx} $, the category of strict
double categories and lax double functors, and characterize a lax double functor into it …

We contribute to the formal theory of pseudomonads, ie the analogue for pseudomonads of
the formal theory of monads. In particular, we solve a problem posed by Steve Lack by …

We show that factorization systems, both strict and orthogonal, can be equivalently
described as double categories satisfying certain properties. This provides conceptual …