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category_of_open_sets [2014/10/28 18:27] nikolaj |
category_of_open_sets [2014/10/28 22:23] nikolaj |
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==== Discussion ==== | ==== Discussion ==== | ||
- | In the category of open sets, If one object $U$ is subset of another $V$, the hom-set $\mathrm{Op}(X)[U,V]=\{i\}$ contains the only inclusion function and is empty otherwise | + | In the category of open sets, if one object $U$ is subset of another $V$, i.e. $U\subseteq V$, the hom-set $\mathrm{Op}(X)[U,V]=\{i\}$ contains the only inclusion function and is empty otherwise. |
=== Reference === | === Reference === | ||
- | nLab: [[http://ncatlab.org/nlab/show/thin+category|Thin category]] | + | Wikipedia: [[http://en.wikipedia.org/wiki/Sheaf_%28mathematics%29|Sheaf]] |
==== Parents ==== | ==== Parents ==== | ||
=== Element of === | === Element of === | ||
[[Cat]], [[Thin category]] | [[Cat]], [[Thin category]] |