Bilimits are Bifinal Objects

TL;DR

This paper characterizes (lax) bilimits in 2-categories using limiting contractions and shows they are equivalent to limiting bifinal objects within the framework of marked 2-categories, enhancing understanding of lax limits.

Contribution

It introduces a new characterization of (lax) bilimits via limiting contractions and establishes their equivalence to bifinal objects in the category of cones.

Findings

Bilimits are characterized by limiting contractions.

Lax bilimits are equivalent to limiting bifinal objects.

Framework applies to various laxity levels, including pseudo-limits.

Abstract

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 limiting bifinal object in the category of cones. Everything is developed in the context of marked 2-categories, so that the machinery can be applied to different levels of laxity, including pseudo-limits.