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1. • CommentRowNumber1.
   • CommentAuthorporton
   • CommentTimeOct 14th 2014
   • (edited Oct 14th 2014)
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   Author: porton
   Format: MarkdownItexIn [topogeny](http://ncatlab.org/toddtrimble/published/topogeny): Lemma 2. Given diagram $\phi: D \to Filt(X)$ with $D$ filtered, $R_X(colim_{d\in D}\; \phi(d), G) = \forall_{d \in D} R_X(\phi(d), G)$. But isn't colimit for a poset (such as $Filt(X)$) just a join (supremum)? And AFAIK, supremum does not depend on whether the diagram $D$ is filtered. What do I misunderstand?

   In topogeny:

   Lemma 2. Given diagram $\phi: D \to Filt(X)$ with $D$ filtered, $R_X(colim_{d\in D}\; \phi(d), G) = \forall_{d \in D} R_X(\phi(d), G)$.

   But isn’t colimit for a poset (such as $Filt(X)$) just a join (supremum)? And AFAIK, supremum does not depend on whether the diagram $D$ is filtered.

   What do I misunderstand?

2. • CommentRowNumber2.
   • CommentAuthorTodd_Trimble
   • CommentTimeOct 14th 2014
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   Author: Todd_Trimble
   Format: MarkdownItexI answered in a private email to Victor.

   I answered in a private email to Victor.