Algebraic weak factorisation systems (awfs) refine weak factorisation systems by requiring
that the assignations sending a map to its first and second factors should underlie an …

Delta lenses are functors equipped with a suitable choice of lifts, and are used to model
bidirectional transformations between systems. In this paper, we construct an algebraic …

We prove a biadjoint triangle theorem and its strict version, which are $2 $-dimensional
analogues of the adjoint triangle theorem of Dubuc. Similarly to the $1 $-dimensional case …

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 …

We establish a correspondence between consistent comprehension schemes and complete
orthogonal factorisation systems. The comprehensive factorisation of a functor between …

We prove that cloven Grothendieck fibrations over a fixed base $\ct {B} $ are the pseudo-
coalgebras for a lax idempotent 2-comonad on $\ct {Cat}/\ct {B} $. We show this via an …

The spectral construction subsumes several prominent mathematical notions, as the
spectrum of a commutative ring in algebraic geometry, or also Stone duality. Interweaving …

In this paper we start by pointing out that Yoneda's notion of a regular span S: X→ A× B can
be interpreted as a special kind of morphism, that we call fiberwise opfibration, in the 2 …

We give an explicit description of the generator of finitely presented objects of the coslice of
a locally finitely presentable category under a given object, as consisting of all pushouts of …

We focus on the transfer of some known orthogonal factorization systems from Cat Cat to the
2-category Fib (B) Fib (B) of fibrations over a fixed base category B: the internal version of …