In the mathematical field of category theory, a section is a morphism which has a left inverse, i.e., a morphism such that is the identity map on N. Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... In mathematics, category theory deals in an abstract way with mathematical structures and relationships between them. ... An identity function f is a function which doesnt have any effect: it always returns the same value that was used as its argument. ...
The categorical concept of a section is important in homological algebra, and is also closely related to the notion of a section of a fiber bundle in topology: in the latter case, the left inverse h is the bundle projection map of the fiber bundle. Homological algebra is the branch of mathematics which studies the methods of homology and cohomology in a general setting. ... In mathematics, in particular in topology, a fiber bundle is a space which locally looks like a product of two spaces but may possess a different global structure. ... In mathematics, in particular in topology, a fiber bundle (or fibre bundle) is a space which locally looks like a product of two spaces but may possess a different global structure. ...
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