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:
“Whatever does not spring from a man’s free choice, or is only the result of instruction and guidance, does not enter into his very being, but still remains alien to his true nature; he does not perform it with truly human energies, but merely with mechanical exactness.”
—Karl Wilhelm Von Humboldt (1767–1835)
“My object all sublime
I shall achieve in time—
To let the punishment fit the crime—
The punishment fit the crime;”
—Sir William Schwenck Gilbert (1836–1911)