nLab
regular monomorphism in an (infinity,1)-category

Contents

Idea

A regular monomorphism in a category is a morphism that is the equalizer of some pair of morphisms. A regular monomorphism in an (,1)(\infty,1)-category is its analog in an (∞,1)-category theory.

Beware that this need not be a monomorphism in an (∞,1)-category.

Definition

Let CC be an (∞,1)-category. A morphism f:xyf : x \to y in CC is a regular monomorphism if there exists a cosimplicial diagram D:ΔCD : \Delta \to C with D[0]=yD[0] = y such that ff is the (∞,1)-limit over this diagram.

xfyy 1y 2 x \stackrel{f}{\to} y \stackrel{\to}{\to} y_1 \stackrel{\to}{\stackrel{\to}{\to}} y_2 \cdots

Revised on October 18, 2010 23:07:47 by Urs Schreiber (131.211.232.170)