Homomorphisms

The basic maps between structures of the same signature K are called homomorphisms, defined as follows. ❋ Hodges, Wilfrid (2009)

In the 1930s Garrett Birkhoff established the fundamental results of equational logic, namely (1) equational classes of algebras are precisely the classes closed under homomorphisms, subalgebras and direct products, and (2) equational logic is based on five rules: reflexivity, symmetry, transitivity, replacement, and substitution. ❋ Burris, Stanley (2009)

Not only does he study systems of objects or whole classes of such systems; and not only does he attempt to identify basic concepts; Dedekind also tends to do both, often in conjunction, by considering mappings on the systems studied, especially structure-preserving mappings (homomorphisms etc.) and what is invariant under them. ❋ Reck, Erich (2008)

Although there are maps between the respective sets of observables, Scheibe considers this as a case of incommensurability, since these maps are not Lie algebra homomorphisms, see Scheibe (1999, 174). ❋ Schmidt, Heinz-Juergen (2008)

Similarly, natural transformations between models of a theory yield the usual homomorphisms of structures in the traditional set theoretical framework. ❋ Marquis, Jean-Pierre (2007)

The notation C (A, B) is generally used to denote the set of all homomorphisms from A to B. ❋ Pratt, Vaughan (2007)

Hence the homomorphisms between B and G compose in either order to identities, which makes them isomorphisms. ❋ Pratt, Vaughan (2007)

The category Grp with objects groups and morphisms group homomorphisms, i.e. (1, ×,?) homomorphisms ❋ Marquis, Jean-Pierre (2007)

However F also maps functions to homomorphisms, mapping f to its unique extension as a homomorphism, while U maps homomorphisms to functions, namely the homomorphism itself as a function. ❋ Pratt, Vaughan (2007)

These four homomorphisms are also closed under composition. ❋ Pratt, Vaughan (2007)

The category AbGrp with objects abelian groups and morphisms group homomorphisms, i.e. (1, ×,?) homomorphisms ❋ Marquis, Jean-Pierre (2007)

The categories Lat and Bool with objects lattices and Boolean algebras, respectively, and morphisms structure preserving homomorphisms, i.e., (Š¤, Š¥, ˆ§, ˆ¨) homomorphisms. ❋ Marquis, Jean-Pierre (2007)

AlgL the Leibniz operator commutes with inverse homomorphisms between algebras in ❋ Jansana, Ramon (2006)

May 23, 2006, 12: 31 am bontril says: bontril homomorphisms. confederation budge. bristle: ❋ Unknown (2004)

L is algebraizable if and only if on the algebra of formulas FmL, the map that sends every theory T to its Leibniz congruence is an isomorphism that commutes with the inverses of homomorphisms from ❋ Jansana, Ramon (2006)

AlgL and morphisms the algebraic homomorphisms are surjective homomorphisms. ❋ Jansana, Ramon (2006)

Then the number of nontrivial group homomorphisms from H to G is ❋ Unknown (2010)

A homomorphism that strikes this balance perfectly is called the 'canonical homomorphism' and the image of the set of all strings under this homomorphisms is called the syntactic monoid. ❋ Unknown (2009)

Most people learning abstract algebra, as far as I can tell, have no idea why homomorphisms and factor groups are sensible things to think about. ❋ Unknown (2009)

Since [sick] has two completely different meanings, [I would] [label] it as a homomorph. ❋ Abraxas Romante (2008)