lax biend



Category theory

Enriched category theory

Limits and colimits



A lax biend is, together with the related notion of a pseudobiend, one of the analogues of ends in 2-category theory.


Similar to how limits are defined as representing objects of the functor Cones ()(D)\mathrm{Cones}_{(-)}(D) of cones over a diagram DD, lax biends are representing objects of a pseudofunctor LaxWedges ()(D)\mathsf{LaxWedges}_{(-)}(D). Below we define all objects involved, arriving at the definition of a lax biend in Section 2.4.

2.1 Preliminaries

In this section we recall some facts and constructions in the setting of bicategories.

2.2 Lax Wedges

Let 𝒞\mathcal{C} and \mathcal{I} be bicategories, D: op×𝒞D\colon\mathcal{I}^\mathrm{op}\times\mathcal{I}\longrightarrow\mathcal{C} be a pseudofunctor, and XX be an object of 𝒞\mathcal{C}.

A lax wedge is a lax extranatural transformation θ:Δ XD\theta\colon\Delta_{X}\overset{\bullet}{\Rightarrow}D from the constant pseudofunctor associated to XX to DD.

2.3 Functoriality of Lax Wedges


2.4 Lax Biends



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