This use of semicolon coincides with the notation for function composition used ( mostly by computer scientists ) in Category theory, as well as the notation for dynamic conjunction within linguistic dynamic semantics.
32.
The composition combinators, often denoted by B _ > for forward composition and B _ for backward composition, are similar to function composition from mathematics, and can be defined as follows:
33.
I'm not talking about factoring here, I'm talking about Function composition, in this case, both being Quadratics yielding a Quartic naturally, I'm quite certain it works.
34.
Since all functions are binary relations, it is correct to use the [ fat ] semicolon for function composition as well ( see the article on composition of relations for further details on this notation ).
35.
The notations,,, etc ., as introduced by John Herschel in 1813, are often used as well, but this convention logically conflicts with the common semantics for expressions like, which refer to numeric power rather than function composition, and therefore may result in confusion between multiplicative inverse and compositional inverse.
36.
The class of all groups with group homomorphisms as morphisms and function composition as the composition operation forms a large category, "'Ab "', consisting of all abelian groups and their group homomorphisms, is a full subcategory of "'Grp "', and the prototype of an abelian category.
37.
Function composition therefore is a useful notion only when the " codomain " of the function on the right side of a composition ( not its " image ", which is a consequence of the function and could be unknown at the level of the composition ) is the same as the domain of the function on the left side.
