nLab
model structure on differential graded-commutative superalgebras

Context

Super-Algebra and Super-Geometry

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

Idea

The category of differential graded-commutative superalgebras over a field of characteristic zero carries a projective model category structure whose weak equivalences are the underlying quasi-isomorphisms and whose fibrations are the degreewise surjections (all either in unbounded degree, in non-negative degree or in non-positive degree).

This is the transferred model structure of the projective model structure on chain complexes of super vector spaces, transferred along the forgetful functor to underlying chain complexes.

The model structure is hence the direct generalization of the projective model structure on differential graded-commutative algebras, to which it reduces on the objects concentrated in even super-degree.

References

A unified treatmeant generalizing to arbitary super Fermat theories is in

Last revised on August 12, 2018 at 18:14:29. See the history of this page for a list of all contributions to it.