In mathematics, the idea of a free object is one of the basic concepts of abstract algebra. It is a part of universal algebra, in the sense that it relates to all types of algebraic structure (with finitary operations). It also has a formulation in terms of category theory, although this is in yet more abstract terms. Examples include free groups, tensor algebras, or free lattices. Informally, a free object over a set A can be thought as being a "generic" algebraic structure over A: the only equations that hold between elements of the free object are those that follow from the defining axioms of the algebraic structure.
Read more about Free Object: Definition, Examples, Free Universal Algebras, Free Functor, List of Free Objects
Famous quotes containing the words free and/or object:
“My job as a reservationist was very routine, computerized ... I had no free will. I was just part of that stupid computer.”
—Beryl Simpson, U.S. employment counselor; former airline reservationist. As quoted in Working, book 2, by Studs Terkel (1973)
“The aim of science is to apprehend this purely intelligible world as a thing in itself, an object which is what it is independently of all thinking, and thus antithetical to the sensible world.... The world of thought is the universal, the timeless and spaceless, the absolutely necessary, whereas the world of sense is the contingent, the changing and moving appearance which somehow indicates or symbolizes it.”
—R.G. (Robin George)