Category theory

Category theory formalizes mathematical structure and its concepts in terms of a collection of objects and of arrows (also called morphisms). Quotes 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 http://books.google.com/books?id=jNClKErmbjMC&pg=PA17 12 November 1975 Academic Press 978-0-08-087380-0 17 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 https://books.google.com/books?id=K-SjOw_2gXwC&pg=PA9 20 October 2005 9 Springer Science & Business Media 978-3-540-27949-5 9– External links Category:Mathematics