nLab
regular (infinity,1)-category

Contents

Contents

Idea

A regular (,1)(\infty,1)-category is the analog of a regular category for (∞,1)-category theory.

Definition

Definition

Let 𝒞\mathcal{C} be an (∞,1)-category. This is called an exact (,1)(\infty,1)-category if

  1. 𝒞\mathcal{C} has a terminal object and homotopy fiber products;

  2. 𝒞\mathcal{C} admits a factorization system (S L,S R)(S_L,S_R), where S LS_L is the collection of regular n-connected morphisms and S RS_R is the collection of n-truncated morphisms.

Last revised on May 17, 2021 at 01:45:25. See the history of this page for a list of all contributions to it.