Complex in an abelian category

A complex in an abelian category is a sequence

\dots \to A_{n + 1} d_{n + 1} A_{n} d_{n} A_{n - 1} \to \dots

with

d_{n} d_{n + 1} = 0

.

Table of contents
- Homology object Complex in an abelian category

Homology object ( $H_{n} (A_{∙})$ )

The homology object is

H_{n} = ker d_{n} / im d_{n + 1}

, formed categorically as the cokernel of the image-to-kernel monomorphism.

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Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 119 / 6 / Solution

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