nLab
cell object

Context

Model category theory

model category

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

Presentation of (,1)(\infty,1)-categories

Model structures

for \infty-groupoids

for ∞-groupoids

for nn-groupoids

for \infty-groups

for \infty-algebras

general

specific

for stable/spectrum objects

for (,1)(\infty,1)-categories

for stable (,1)(\infty,1)-categories

for (,1)(\infty,1)-operads

for (n,r)(n,r)-categories

for (,1)(\infty,1)-sheaves / \infty-stacks

Contents

Definition

For (LR):CRLD(L \dashv R) : C \stackrel{\overset{L}{\leftarrow}}{\underset{R}{\to}} D a pair of adjoint functors between model categories CC and DD, an object XCX \in C is an LL-cell object if it is connected to the initial object by a (possibly transfinite) composition of pushouts of morphisms of the form L(f)L(f).

References

Definition 3.2 in

Created on November 3, 2010 22:41:52 by Urs Schreiber (87.212.203.135)