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• CommentRowNumber1.
• CommentAuthorDavidRoberts
• CommentTimeJul 22nd 2019

Formatting fix

• CommentRowNumber2.
• CommentAuthorDmitri Pavlov
• CommentTimeAug 27th 2022
• (edited Aug 27th 2022)

## Terminology

In older literature, such as the original work of Bousfield–Kan \cite{BousfieldKan}, the homotopy limit of a diagram $X\colon I\to sSet$ is defined as the weighted limit

$hom(I/-, X),$

where the weight $I/-$ sends $i\mapsto N(I/i)$, the nerve of the comma category of $i$.

Such a functor must be derived in order to get the correct (homotopy invariant) notion, which in this case amounts to replacing $X$ with an objectwise weakly equivalent diagram valued in Kan complexes.

At some point (when?) a shift in terminology happened, and in the modern parlance homotopy limits are commonly assumed to be derived.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeAug 27th 2022

I have added to this addition (here) a link to Bousfield-Kan map and also to the entry’s own section “Resolved (co)ends”.