Related papers: Lax structures in 2-category theory

We define the notion of 2-filtered 2-category and give an explicit construction of the bicolimit of a category valued 2-functor. A category considered as a trivial 2-category is 2-filtered if and only if it is a filtered category, and our…

We study Quillen model categories equipped with a monoidal skew closed structure that descends to a genuine monoidal closed structure on the homotopy category. Our examples are 2-categorical and include permutative categories and…

We continue our study of semi-strict tricategories in which the only weakness is in vertical composition. We assemble the doubly-degenerate such tricategories into a 2-category, defining weak functors and transformations. We exhibit a…

In this thesis weighted colimits in 2-categories equipped with promorphisms are studied. Such colimits include most universal constructions with counits, like ordinary colimits in categories, weighted colimits in enriched categories, and…

We extend the notion of a factorization system in a category to the realm of $\infty$-categories. To this end, we provide a description of the category of $\infty$-categories with factorization systems as the category of presheaves of…

We extend the classical work of Kock on strong and commutative monads, as well as the work of Hyland and Power for 2-monads, in order to define strong and pseudocommutative relative pseudomonads. In order to achieve this, we work in the…

For a small quantaloid $\mathcal{Q}$, we consider 2-monads on the 2-category $\mathcal{Q}$-$\bf{Cat}$ and their lax extensions to the 2-category $\mathcal{Q}$-$\bf{Dist}$ of small $\mathcal{Q}$-categories and their distributors, in…

We prove that a (lax) bilimit of a 2-functor is characterized by the existence of a limiting contraction in the 2-category of (lax) cones over the diagram. We also investigate the notion of bifinal object and prove that a (lax) bilimit is a…

In the first part, we further advance the study of category theory in a strong balanced factorization category C [Pisani, 2008], a finitely complete category endowed with two reciprocally stable factorization systems such that X \to 1 is in…

We study the duplicial objects of Dwyer and Kan, which generalize the cyclic objects of Connes. We describe duplicial objects in terms of the decalage comonads, and we give a conceptual account of the construction of duplicial objects due…

We categorify cocompleteness results of monad theory, in the context of pseudomonads. We first prove a general result establishing that, in any 2-category, weighted bicolimits can be constructed from oplax bicolimits and bicoequalizers of…

The structure of the category of matroids and strong maps is investigated: it has coproducts and equalizers, but not products or coequalizers; there are functors from the categories of graphs and vector spaces, the latter being faithful;…

We study the 2-category of elements from an abstract point of view. We generalize to dimension 2 the well-known result that the category of elements can be captured by a comma object that also exhibits a pointwise left Kan extension. For…

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 obtaining a lax double quasi-functor. The latter consists of a…

A 2-categorical generalisation of elementary topos is provided and some of the properties of the yoneda structure it generates are explored. Examples relevant to the globular approach to higher category theory are discussed. This paper also…

We introduce the notion of a relative pseudomonad, which generalises the notion of a pseudomonad, and define the Kleisli bicategory associated to a relative pseudomonad. We then present an efficient method to define pseudomonas on the…

We define strict and lax orthogonal factorization systems on double categories. These consist of an orthogonal factorization system on arrows and one on double cells that are compatible with each other. Our definitions are motivated by…

This paper shows how internal models for polymorphic lambda calculi arise in any 2-category with a notion of discreteness. We generalise to a 2-categorical setting the famous theorem of Peter Freyd saying that there are no sufficiently…

We define a notion of category enriched over an oplax monoidal category $V$, extending the usual definition of category enriched over a monoidal category. Even though oplax monoidal structures involve infinitely many functors $V^n\to V$,…

Originally introduced in the context of the algebraic approach to term graph rewriting, the notion of gs-monoidal category has surfaced a few times under different monikers in the last decades. They can be thought of as symmetric monoidal…