In mathematics, more specifically in cohomology theory, a q {\displaystyle q\,\!} -cocycle α {\displaystyle \alpha \,\!} in the cochain group S q ( X ) {\displaystyle S^{q}(X)\,\!} is associated with a unique equivalence class [ α ] ∈ H q ( X ) {\displaystyle [\alpha ]\in H^{q}(X)\,\!} known as the cocycle class or coclass of α . {\displaystyle \alpha .\,\!}
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![[\alpha ]\in H^{q}(X)\,\!](https://wikimedia.org/api/rest_v1/media/math/render/svg/1c1f943e3a675ab9942a3c8110ee21f52eac6a41)
