Background
Basic concepts
equivalences in/of $(\infty,1)$-categories
Universal constructions
Local presentation
Theorems
Extra stuff, structure, properties
Models
A regular $(\infty,1)$-category is the analog of a regular category for (∞,1)-category theory.
Let $\mathcal{C}$ be an (∞,1)-category. This is called an exact $(\infty,1)$-category if
$\mathcal{C}$ has a terminal object and homotopy fiber products;
$\mathcal{C}$ admits a factorization system $(S_L,S_R)$, where $S_L$ is the collection of regular n-connected morphisms and $S_R$ is the collection of n-truncated morphisms.
An (∞,1)-category $C$ is regular if it admits finite (∞,1)-limits, every morphism in $C$ has an image, i.e., can be written as a composition of an (∞,1)-quotient morphism and an (∞,1)-monomorphism, and the collection of (∞,1)-quotient morphisms is closed under base changes.
exact (infinity,1)-category, coherent (infinity,1)-category?, (infinity,1)-pretopos
infinity-allegory?
Last revised on December 14, 2023 at 20:46:17. See the history of this page for a list of all contributions to it.