nLab graded-cocommutative differential coalgebra

Definition

A graded-cocommutative differential coalgebra is a cocommutative coalgebra in the category of chain complexes (of modules over some ring).

We write $GCDC$ for the category of such codifferential coalgebras.

Remarks

• Differential coalgebras whose underlying graded-cocommutative coalgebra is free over a complex of vector spaces in positive degree are Lie infinity-algebras.

Related concepts

• coalgebra, differential graded coalgebra

References

• Ezra Getzler and Paul Goerss, A model category structure for differential graded coalgebras (ps)

Blog resources

• Todd Trimble, nice facts about CoDGCA

• Todd Trimble, Sketch of proof that CoDGCA is cartesian closed

category: category