More generally, a regular monomorphism in any category is any morphism m that is an equalizer of some set of morphisms. This page was last edited on 6 Decemberat In the case of a preadditive category a eq binare enriched over the category of Abelian groupsthe term "difference kernel" may be interpreted literally, since subtraction of morphisms makes eq binare. In more explicit terms, the equalizer consists of an object E and a morphism eq binare
The definition above used eq binare functions f eq binare gbut there is no need to restrict to only two functions, or even to only finitely many functions. Free category Functor category Quotient category Product category Subcategory. Let X and Y be sets. However, if the category in question is completethen both definitions agree.
These objects and morphisms form a diagram in the category in question, and the equalizer is simply the limit of that diagram. Retrieved from eq binare https: The last notation shows where this terminology comes from, and why it is most common in the context of abstract algebra: Eq binare equalizer may be denoted Eq fg or a variation on that theme such as with lowercase letters "eq". In the general context, X and Y are objects, while f and g are morphisms from X to Eq binare.
Then the equalizer of f and g is the set of elements x of X such that f eq binare equals g x in Y. The generalization of this to more than two morphisms is straightforward; simply use a larger diagram with more morphisms in it. Eq binare last notation shows where this terminology eq binare from, and why it is most common in the context of abstract algebra: From Wikipedia, the free encyclopedia. The degenerate case of only one morphism is also straightforward; then eq can be any isomorphism from an object E to X.
Eq binare category Functor category Quotient category Product category Subcategory. This page was last edited on 6 Decemberat In any universal algebraic category, including eq binare categories where difference kernels are used, as well as the category of sets itself, the object E can always be taken to be the ordinary notion of equalizer, and the morphism eq can in that case eq binare taken to be the inclusion function of E as a subset of X. Views Read Edit View history.
The correct diagram for the degenerate case with no morphisms is slightly subtle: This page was last edited on 6 Decemberat The last notation eq binare where this terminology comes from, and why it is most common in the context of abstract algebra: Eq binare mathematicsan equalizer is a set of arguments where two or more functions have equal values.