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Definitions from the Web

Cohomology

Definition:

Cohomology is a mathematical concept used to measure the topological properties of spaces or objects. It is a branch of algebraic topology that studies the relative relationships of cycles and boundaries in a space.

Senses:

Noun

1. Homology Cohomology: In mathematics, homology cohomology is a pair of mathematical theories closely related to each other. They are used to study the properties of geometric objects by associating algebraic structures to them.

Example sentence: The study of homology cohomology has greatly advanced our understanding of complex geometric shapes.

2. Sheaf Cohomology: Sheaf cohomology is a branch of algebraic topology that deals with the study of cohomology groups of sheaves. It has applications in various fields, including differential geometry and algebraic geometry.

Example sentence: Sheaf cohomology provides a powerful tool for understanding the global properties of sheaves on geometric spaces.

Adjective

1. Cohomological: Pertaining to or related to cohomology.

Example sentence: The research paper presented a cohomological approach to understanding the behavior of certain mathematical structures.

Verb

1. Cohomologize: To apply cohomology theory or methods to a mathematical problem.

Example sentence: The mathematician decided to cohomologize the problem in order to gain deeper insights into its solution.

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