For: Canonical Ltd.

Canonical is an adjective derived from canon. Canon comes from the Greek word kanon, "rule" (perhaps originally from kanna "reed", cognate to cane), and is used in various meanings.

Basic, canonic, canonical: reduced to the simplest and most significant form possible without loss of generality, e.g., "a basic story line"; "a canonical syllable pattern."

Religion

This word is used by theologians and canon lawyers to refer to the canons of the Roman Catholic, Eastern Orthodox and Anglican Churches adopted by ecumenical councils. It also refers to later law developed by local churches and dioceses of these churches. The function of this collection of various "canons" is somewhat analogous to the precedents established in common law by case law.

In the 20th century, the Roman Catholic Church revised its canon law in 1917 and then again 1983 into the modern Code of Canon Law. This code is no longer merely a compilation of papal decrees and conciliar legislation, but a more completely developed body of international church law. It is analogous to the English system of statute law.

Canonical can also mean "part of the canon", i.e., one of the books comprising a biblical canon, as opposed to apocryphal books.

The term is also applied by Westerners to other religions, but in inconsistent ways: for example, in the case of Buddhism one authority refers to "scriptures and other canonical texts", while another says that scriptures can be categorized into canonical, commentarial and pseudo-canonical.

Canonization is the process by which a person becomes recognized as a saint.

Literature and art

The word is also often used when describing bodies of literature or art: those books that all educated people have supposedly read, or are advised to read, make up the "canon", for example the Western canon. (See also canon (fiction)).

Mathematics

Mathematicians have for perhaps a century or more used the word canonical to refer to concepts that have a kind of uniqueness or naturalness, and are (up to trivial aspects) "independent of coordinates." Examples include the canonical prime factorization of positive integers, the Jordan canonical form of matrices (which is built out of the irreducible factors of the characteristic polynomial of the matrix), and the canonical decomposition of a permutation into a product of disjoint cycles. Various functions in mathematics are also canonical, like the canonical homomorphism of a group onto any of its quotient groups, or the canonical isomorphism between a finite-dimensional vector space and its double dual. Although a finite-dimensional vector space and its dual space are isomorphic, there is no canonical isomorphism. This lack of a canonical isomorphism can be made precise in terms of category theory; see natural transformation. But at a simpler level one could say that "any isomorphism you can think of here depends on choosing a basis." As stated by Goguen, "To any canonical construction from one species of structure to another corresponds an adjunction between the corresponding categories."