Morphism
Morphism In mathematics, a morphism is an abstraction of a structure-preserving ... There are two operations defined on every morphism, the domain (or source) and the codomain ... to their codomain, e.g. if a morphism f has domain X and codomain Y ... for every object X, there exists a morphism id X : X → X called ...
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Monic
Monic In mathematics, monic can refer to monic morphism – a special kind of morphism in category theory, monic polynomial – ...
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Category theory
... object of another category; and to every morphism in the first category a morphism in the second. By studying categories and ... Categories, objects, and morphisms Main articles: category, morphism A category C consists of a class ... a class hom(C) of morphisms. Each morphism f has a unique source object a ... b, and we say "f is a morphism from a to b". We write ...
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Category (mathematics)
... a class hom(C) of morphisms. Each morphism f has a unique source object a ... b, and we say "f is a morphism from a to b". We write hom ... for every object x, there exists a morphism 1 x : x → x called the identity morphism for x, such that for every morphism f : a → b, we have ...
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Image (category theory)
... theory) Given a category C and a morphism $f:X\backslash rightarrow\; Y$ in ... the following universal property: There exists a morphism $g:X\backslash rightarrow\; I$ such ... hg. For any object Z with a morphism $k:X\backslash rightarrow\; Z$ and ... that f = lk, there exists a unique morphism $m:I\backslash rightarrow\; Z$ such ... Im(f). One can show that a morphism f is monic if and only ...
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Monomorphism
... category theory, a monomorphism (also called a monic morphism or a mono) is a morphism f : X → Y such that f ... While this is not exactly true for monic maps, it is very close, so this ... underlying maps of sets were injective, and monic maps, which are monomorphisms in the ...
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User:Lethe/list of categories
... n n n n all morphisms are monic Frm frames defined to be the opposite ... y n n 1 one object identity morphism z:0 n n n 2 i ... 1: The one object category with one morphism 2: The two object category with one morphism not an identity between the distinct objects ...
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Isomorphism   (translated from French)
... Algebrist In algèbre , one isomorphism is one morphism bijectif . In other words, it is a ... of the categories one isomorphism is a morphism which has one opposite on the left ... morphisms at the same time epic and monic which are not isomorphisms. For more details ...
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Subobject
... ≤ v when u = vu′ for some morphism u′ : S → T. We also write ... that is, to define quotient object replace monic by epic above and reverse arrows. Examples ... arrows in such a category will be monic. See also subobject classifier
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Order-embedding
... that a section s is just a morphism that has a left-inverse r (called ... to injectivity (implying that a mapping is monic), one needs reflection of the order to ...
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