Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 165 / 2 / i / Solution

For a simplicial abelian group $A$, its normalized chain complex of a simplicial abelian group isThe simplicial identities give ${\partial }^2=0$. Equivalently, $N_{n}A$ is the quotient of $A_n$ by the subgroup generated by degenerate simplices, with differential induced by ${\sum }_i(-1{)}^i{d}_i$.

Solved by gpt-5.6-sol high.