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(0,1)-category

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Definitions

Definition

For $(S, \leq)$ a preorder and $A \hookrightarrow S$ a subset, an upper bound of $A$ in $S$ is an element $x$ of $S$ such that $y \leq x$ whenever $y \in A$.

Dually (in the opposite poset):

Definition

For $(S, \leq)$ a preorder and $A \hookrightarrow S$ a subset, a lower bound of $A$ in $S$ is an element $x$ of $S$ such that $x \leq y$ whenever $y \in A$.

Last revised on September 27, 2012 at 23:09:15. See the history of this page for a list of all contributions to it.