Category of Sets

In the mathematical field of category theory, the category of sets, denoted as Set, is the category whose objects are sets. The arrows or morphisms between sets A and B are all functions from A to B. Care must be taken in the definition of Set to avoid set-theoretic paradoxes.

Many other categories (such as the category of groups, with group homomorphisms as arrows) add structure to the objects of the category of sets and/or restrict the arrows to functions of a particular kind.

Read more about Category Of Sets:  Properties of The Category of Sets, Foundations For The Category of Sets

Famous quotes containing the words category of, category and/or sets:

    Despair is typical of those who do not understand the causes of evil, see no way out, and are incapable of struggle. The modern industrial proletariat does not belong to the category of such classes.
    Vladimir Ilyich Lenin (1870–1924)

    Despair is typical of those who do not understand the causes of evil, see no way out, and are incapable of struggle. The modern industrial proletariat does not belong to the category of such classes.
    Vladimir Ilyich Lenin (1870–1924)

    The world can doubtless never be well known by theory: practice is absolutely necessary; but surely it is of great use to a young man, before he sets out for that country, full of mazes, windings, and turnings, to have at least a general map of it, made by some experienced traveller.
    Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)