Chain complex of groups bounded from above

This article defines a chain complex property, i.e., a property that can be evaluated to true/false for any given chain complex of groups. See all properties of chain complexes of groups

Definition

Consider a chain complex of groups $(G_{n},d_{n})_{n\in \mathbb {Z} }$. We say that this chain complex is bounded from above if there exist an integers $n_{0}\in \mathbb {Z}$ such that $G_{n}$ is the trivial group for all $n\geq n_{0}$.

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
bounded chain complex of groups				|FULL LIST, MORE INFO