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Composition of Morphisms

The composition of morphisms f:X->Y and g:Y->Z in a category is the morphism g degreesf:X->Z. Composition is associative and each object has an identity morphism that acts as a left and right identity.

For schemes, composition is obtained by composing the underlying continuous maps and the compatible maps of structure sheaves.

See also

Category, Function Composition, Morphism, Scheme

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References

Mac Lane, S. Categories for the Working Mathematician, 2nd ed. New York: Springer-Verlag, 1998.

Cite this as:

Weisstein, Eric W. "Composition of Morphisms." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CompositionofMorphisms.html

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