Identical Variety

Let \(\circ\) be Identity. For variety, let \(c-\circ\) and \(\circ-C\) be named as Complementary Identities of \(\circ\). To simplify terminology, let us name these to be Identical Varieties. Thus, corresponding to the Identity \(\circ\), we have Identical Varieties \(c-\circ\), \(\circ\) and \(\circ-C\). In usual language, let the Complementary (relative to \(\circ\)) identities \(c-\circ\) and \(\circ-C\) in the Identical Variety be called \(c\)-Identities.

Variety Identical (Examples)

  • For example: The statement “Identities are identified by Identification” may be expressed in terms of Identical Varieties.

  • Identities act as objects and naming acts as the Identification. Thus Corresponding to Identities, let us name objects as the \(c-\circ\) and identification as \(\circ-C\).

  • In Category theory, let objects be named as the Identity \(\circ\), morphisms be named as the Complementary Identity \(c-\circ\) and the Category be named as \(\circ-C\). For variety, let objects be named as the complementary identity \(c-\circ\), morphisms be named as \(\circ-C\) and the Category be named as the Identity \(\circ\). For variety, let morphisms be named as the Identity \(\circ\), the Category be named as the Complementary Identity \(c-\circ\) and the objects be named as \(\circ-C\).

  • In Physics, let ‘Laws of Physics’ be named as the Identity \(\circc\), theories in Physics be named as Complementary Identities. For historical reasons, the word ‘Relative’ is often used in place of ‘Complementary’.