nLab
linear model category

Contents

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 rational \infty-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

Stable homotopy theory

Contents

Definition

A model category is called linear if it has a zero object (is a “pointed category” and hence a pointed model category) and for all of its objects XX, the unit

XΩΣX X \stackrel{\simeq}{\longrightarrow} \Omega \Sigma X

of the (reduced suspension \dashv loop space object)-adjunction is a weak equivalence.

(Schwede 97, def. 2.2.1)

References

Last revised on January 31, 2021 at 03:08:23. See the history of this page for a list of all contributions to it.