English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Consider a diagram of quasi-categories that admit and functors that preservelimits or colimits of a fixed shape. We show that any weighted limit whoseweight is a projective cofibrant simplicial functor is again a quasi-categoryadmitting these (co)limits and that they are preserved by the functors in thelimit cone. In particular, the Bousfield-Kan homotopy limit of a diagram ofquasi-categories admit any limits or colimits existing in and preserved by thefunctors in that diagram. In previous work, we demonstrated that thequasi-category of algebras for a homotopy coherent monad could be described asa weighted limit with projective cofibrant weight, so these results immediatelyprovide us with important (co)completeness results for quasi-categories ofalgebras. These generalise most of the classical categorical results, exceptfor a well known theorem which shows that limits lift to the category ofalgebras for any monad, regardless of whether its functor part preserves thoselimits. The second half of this paper establishes this more general result inthe quasi-categorical setting: showing that the monadic forgetful functor ofthe quasi-category of algebras for a homotopy coherent monad creates all limitsthat exist in the base quasi-category, without further assumption on the monad.This proof relies upon a more delicate and explicit analysis of the particularweight used to define quasi-categories of algebras.

Completeness results for quasi-categories of algebras, homotopy limits, and related general constructions