Relation To Other Categorical Concepts
Let C and D be categories. The collection of all functors C→D form the objects of a category: the functor category. Morphisms in this category are natural transformations between functors.
Functors are often defined by universal properties; examples are the tensor product, the direct sum and direct product of groups or vector spaces, construction of free groups and modules, direct and inverse limits. The concepts of limit and colimit generalize several of the above.
Universal constructions often give rise to pairs of adjoint functors.
Read more about this topic: Functor
Famous quotes containing the words relation to, relation, categorical and/or concepts:
“The difference between objective and subjective extension is one of relation to a context solely.”
—William James (18421910)
“The psychoanalysis of individual human beings, however, teaches us with quite special insistence that the god of each of them is formed in the likeness of his father, that his personal relation to God depends on his relation to his father in the flesh and oscillates and changes along with that relation, and that at bottom God is nothing other than an exalted father.”
—Sigmund Freud (18561939)
“We do the same thing to parents that we do to children. We insist that they are some kind of categorical abstraction because they produced a child. They were people before that, and theyre still people in all other areas of their lives. But when it comes to the state of parenthood they are abruptly heir to a whole collection of virtues and feelings that are assigned to them with a fine arbitrary disregard for individuality.”
—Leontine Young (20th century)
“Germany collapsed as a result of having engaged in a struggle for empire with the concepts of provincial politics.”
—Albert Camus (19131960)