Given a pseudomonad $mathcal{T} $ on a $2$-category $mathfrak{B} $, if a right biadjoint $mathfrak{A}tomathfrak{B} $ has a lifting to the pseudoalgebras $mathfrak{A}tomathsf{Ps}textrm{-}mathcal{T}textrm{-}mathsf{Alg} $ then this lifting is also right biadjoint provided that $mathfrak{A} $ has codescent objects. In this paper, we give  general results on lifting of biadjoints. As a consequence, ...

Abstract Let $${\mathbb {A}}$$ A be a 2-category with suitable opcomma objects and pushouts. We give direct proof that, provided that the codensity monad of morphism p exists is preserved by morphism, factorization given lax descent object two-dimensional cokernel diagram up to isomorphism same as semantic , ...

We find a criterion for a morphism of coalgebras over a Barr-exact category to be effective descent and determine (effective) descent morphisms for coalgebras over toposes in some cases. Also, we study some exactness properties of endofunctors of arbitrary categories in connection with natural transformations between them as well as those of functors that these transformations induce between co...

we find a criterion for a morphism of coalgebras over a barr-exact category to be effective descent and determine (effective) descent morphisms for coalgebras over toposes in some cases. also, we study some exactness properties of endofunctors of arbitrary categories in connection with natural transformations between them as well as those of functors that these transformations induce between co...

In this paper we investigate effective descent morphisms in categories of reflexive and transitive lax algebras. We show in particular that open and proper maps are effective descent, result that extends the corresponding results for the category of topological spaces and continuous maps. Introduction A morphism p : E → B in a category C with pullbacks is called effective descent if it allows a...

Introduction In this paper we prove a conjecture of Andrew Pitts which states that the Beck Chevalley condition holds for lax pullbacks or comma squares of coherent toposes see Theorem below Pitts conjecture was put forward as a way towards the lax descent theorem for coherent toposes Theorem below The latter entails a dual version for pretoposes which was eventually established by Zawadowski i...

We prove that there is a full and faithful nerve functor defined on the category 2-Cat lax of 2-categories and (normal) lax 2-functors. This functor extends the usual notion of nerve of a category and it coincides on objects with the so-called geometric nerve of a 2-category or of a 2-groupoid. We also show that (normal) lax 2-natural transformations produce homotopies of a special kind, and th...