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category_._set_theory [2014/04/07 19:06]
nikolaj old revision restored (2014/04/07 17:19)
category_._set_theory [2014/10/28 18:09] (current)
nikolaj
Line 6: Line 6:
 | @#FF9944: definition ​ | @#FF9944: $\circ:​{\large\prod}_{A,​B,​C:​\mathcal{O}}\,​\mathrm{Mor}(B,​C)\times\mathrm{Mor}(A,​B)\to\mathrm{Mor}(A,​C)$ | | @#FF9944: definition ​ | @#FF9944: $\circ:​{\large\prod}_{A,​B,​C:​\mathcal{O}}\,​\mathrm{Mor}(B,​C)\times\mathrm{Mor}(A,​B)\to\mathrm{Mor}(A,​C)$ |
 | @#FF9944: definition ​ | @#FF9944: $id:​{\large\prod}_{A:​\mathcal{O}}\,​\mathrm{Mor}_O(A,​A)$ | | @#FF9944: definition ​ | @#FF9944: $id:​{\large\prod}_{A:​\mathcal{O}}\,​\mathrm{Mor}_O(A,​A)$ |
-| @#55EE55: postulate ​  | @#55EE55: $\mathrm{Mor}(A,​B)\cap\mathrm{Mor}(U,​V)\ne\emptyset\implies ​A=B\land U=V$ |+| @#55EE55: postulate ​  | @#55EE55: $\mathrm{Mor}(A,​B)\cap\mathrm{Mor}(U,​V)\ne\emptyset\implies ​U=A\land V=B$ |
 | @#55EE55: postulate ​  | @#55EE55: $(g\circ f)\circ h=g\circ (f\circ h)$ | | @#55EE55: postulate ​  | @#55EE55: $(g\circ f)\circ h=g\circ (f\circ h)$ |
 | @#55EE55: postulate ​  | @#55EE55: $f\circ id_A=id_A\circ f=f$ | | @#55EE55: postulate ​  | @#55EE55: $f\circ id_A=id_A\circ f=f$ |
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