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equivalence_of_categories [2014/11/01 17:55] nikolaj |
equivalence_of_categories [2014/12/04 22:34] nikolaj |
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| ==== Collection ==== | ==== Collection ==== | ||
| | @#55CCEE: context | @#55CCEE: ${\bf C},{\bf D}$ ... categories | | | @#55CCEE: context | @#55CCEE: ${\bf C},{\bf D}$ ... categories | | ||
| - | | @#FFBB00: definiendum | @#FFBB00: $F$ in ${\bf C}\simeq{\bf D}$ | | + | | @#FFBB00: definiendum | @#FFBB00: $F$ in ${\bf D}\simeq{\bf C}$ | |
| | @#AAFFAA: inclusion | @#AAFFAA: $F$ in ${\bf D}\longrightarrow{\bf C}$ | | | @#AAFFAA: inclusion | @#AAFFAA: $F$ in ${\bf D}\longrightarrow{\bf C}$ | | ||
| | @#FFFDDD: exists | @#FFFDDD: $G$ in ${\bf C}\longrightarrow{\bf D}$ | | | @#FFFDDD: exists | @#FFFDDD: $G$ in ${\bf C}\longrightarrow{\bf D}$ | | ||
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| === Elaboration === | === Elaboration === | ||
| Here $Id_{\bf C}$ denotes the [[identity functor]] on ${\bf C}$. | Here $Id_{\bf C}$ denotes the [[identity functor]] on ${\bf C}$. | ||
| - | |||
| - | === In words === | ||
| - | Two categories are equivalent, if there is are functors $F,G$ mediating between them, which don't deform them too much: They are tame enough so that their composite deformations can be repaired back to unity. | ||
| === Motivation === | === Motivation === | ||
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| ==== Parents ==== | ==== Parents ==== | ||
| === Context === | === Context === | ||
| - | [[Category]] | + | [[Categories]] |
| === Requirements === | === Requirements === | ||
| [[Natural isomorphism]], [[Identity functor]] | [[Natural isomorphism]], [[Identity functor]] | ||
