Dual of a chain complex: differentials dⁿ: Cⁿ → Cⁿ⁺¹ with dⁿ⁺¹ dⁿ = 0. Cohomology Hⁿ = ker dⁿ / im dⁿ⁻¹ carries a contravariant functorial structure and a cup-product when the underlying complex does.
Dual of a chain complex: differentials dⁿ: Cⁿ → Cⁿ⁺¹ with dⁿ⁺¹ dⁿ = 0. Cohomology Hⁿ = ker dⁿ / im dⁿ⁻¹ carries a contravariant functorial structure and a cup-product when the underlying complex does.