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- Image_(category_theory) abstract "Given a category C and a morphism in C, the image of f is a monomorphism satisfying the following universal property:There exists a morphism such that f = hg.For any object Z with a morphism and a monomorphism such that f = lk, there exists a unique morphism such that h = lm.Remarks: such a factorization does not necessarily exist g is unique by definition of monic (= left invertible, abstraction of injectivity) m is monic. h=lm already implies that m is unique. k=mgFile:Image diagram category theory.svgThe image of f is often denoted by im f or Im(f).One can show that a morphism f is monic if and only if f = im f.".
- Image_(category_theory) thumbnail Image_diagram_category_theory.svg?width=300.
- Image_(category_theory) wikiPageID "342899".
- Image_(category_theory) wikiPageRevisionID "603742438".
- Image_(category_theory) hasPhotoCollection Image_(category_theory).
- Image_(category_theory) subject Category:Category_theory.
- Image_(category_theory) comment "Given a category C and a morphism in C, the image of f is a monomorphism satisfying the following universal property:There exists a morphism such that f = hg.For any object Z with a morphism and a monomorphism such that f = lk, there exists a unique morphism such that h = lm.Remarks: such a factorization does not necessarily exist g is unique by definition of monic (= left invertible, abstraction of injectivity) m is monic. h=lm already implies that m is unique.".
- Image_(category_theory) label "Bild (Kategorientheorie)".
- Image_(category_theory) label "Image (category theory)".
- Image_(category_theory) sameAs Bild_(Kategorientheorie).
- Image_(category_theory) sameAs m.01ybf7.
- Image_(category_theory) sameAs Q860530.
- Image_(category_theory) sameAs Q860530.
- Image_(category_theory) wasDerivedFrom Image_(category_theory)?oldid=603742438.
- Image_(category_theory) depiction Image_diagram_category_theory.svg.
- Image_(category_theory) isPrimaryTopicOf Image_(category_theory).
