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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] nikolaj |
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| | @#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: $f\circ id_A=id_A\circ f=f$ | | ||
