![]() ![]() ![]() One often says that a morphism is an arrow that maps its source to its target. Examples include quotient spaces, direct products, completion, and duality.Ī category is formed by two sorts of objects, the objects of the category, and the morphisms, which relate two objects called the source and the target of the morphism. In particular, many constructions of new mathematical objects from previous ones, that appear similarly in several contexts are conveniently expressed and unified in terms of categories. Nowadays, category theory is used in almost all areas of mathematics, and in some areas of computer science. (The category's three identity morphisms 1 X, 1 Y and 1 Z, if explicitly represented, would appear as three arrows, from the letters X, Y, and Z to themselves, respectively.)Ĭategory theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Schematic representation of a category with objects X, Y, Z and morphisms f, g, g ∘ f. ![]()
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