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- Isomorphism_of_categories abstract "In category theory, two categories C and D are isomorphic if there exist functors F : C → D and G : D → C which are mutually inverse to each other, i.e. FG = 1D (the identity functor on D) and GF = 1C. This means that both the objects and the morphisms of C and D stand in a one to one correspondence to each other. Two isomorphic categories share all properties that are defined solely in terms of category theory; for all practical purposes, they are identical and differ only in the notation of their objects and morphisms.Isomorphism of categories is a very strong condition and rarely satisfied in practice. Much more important is the notion of equivalence of categories; roughly speaking, for an equivalence of categories we don't require that FG(x) be equal to x, but only isomorphic to x in the category D, and likewise that GF(y) be isomorphic to y in C.".
- Isomorphism_of_categories wikiPageID "489935".
- Isomorphism_of_categories wikiPageRevisionID "332016796".
- Isomorphism_of_categories hasPhotoCollection Isomorphism_of_categories.
- Isomorphism_of_categories subject Category:Adjoint_functors.
- Isomorphism_of_categories comment "In category theory, two categories C and D are isomorphic if there exist functors F : C → D and G : D → C which are mutually inverse to each other, i.e. FG = 1D (the identity functor on D) and GF = 1C. This means that both the objects and the morphisms of C and D stand in a one to one correspondence to each other.".
- Isomorphism_of_categories label "Isomorphism of categories".
- Isomorphism_of_categories sameAs m.02gq0b.
- Isomorphism_of_categories sameAs Q6086107.
- Isomorphism_of_categories sameAs Q6086107.
- Isomorphism_of_categories wasDerivedFrom Isomorphism_of_categories?oldid=332016796.
- Isomorphism_of_categories isPrimaryTopicOf Isomorphism_of_categories.