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The graded ring formed by cohomology groups with multiplication given by the cup product.
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This is an authored directed relation from the source endpoint to the target endpoint.
With ring coefficients, collect the groups over all degrees and equip their graded direct sum with the cup product.
Equip an existing carrier or structured object with additional chosen data, when such compatible data exists. Use a construction junction when several independently meaningful inputs must coexist on the same carrier or interact compatibly.
hatcher-algebraic-topologyEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
The cup product equips the direct sum of cohomology groups with a graded ring structure; forgetting multiplication leaves a graded object.
Pass canonically from a stronger object to structure it determines, or forget part of the data while retaining a valid weaker structure. The carrier may change under a canonical induced construction.
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