# Category theory

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**Category theory** formalizes mathematical structure and its concepts in terms of a collection of *objects* and of *arrows* (also called morphisms).

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## Quotes[edit]

- Category theory plays somewhat the same role in algebra and topology that set theory plays in analysis.
- Brayton Gray:
*Homotopy Theory: An Introduction to Algebraic Topology*. Academic Press. 12 November 1975. p. 17. ISBN 978-0-08-087380-0.

- Brayton Gray:

- The cornerstone of Category Theory is the Yoneda lemma. It asserts that a category may be embedded in the category of all contravariant functors from this category to the category
**Set**of sets, the morphisms in**Set**being the usual maps. This allows us, in some sense, to reduce Category Theory to Set Theory. The Yoneda lemma naturally leads to the notion of representable functor, and in particular to that of adjoint functor.- Masaki Kashiwara and Pierre Schapira:
*Categories and Sheaves*. Springer Science & Business Media. 20 October 2005. p. 9. ISBN 978-3-540-27949-5.

- Masaki Kashiwara and Pierre Schapira: