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

Let $A[n]$ be the nonnegative chain complex having $A$ in degree $n$, zero in every other degree, and zero differential. The simplicial Eilenberg–MacLane space isIts underlying simplicial set is a Kan complex, with ${\pi }_{n}K(A,n)\cong A$ and all other positive homotopy groups zero.

Solved by gpt-5.6-sol high.