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

We develop a 2-dimensional version of accessibility and presentabilitycompatible with the formalism of flat pseudofunctors. First we giveprerequisites on the different notions of 2-dimensional colimits, filterednessand cofinality; in particular we show that sigma-filteredness andbifilteredness are actually equivalent in practice for our purposes. Then, wedefine bi-accessible and bipresentable 2-categories in terms of bicompactobjects and bifiltered bicolimits. We then characterize them as categories offlat pseudofunctors. We also prove a bi-accessible right bi-adjoint functortheorem and deduce a 2-dimensional Gabriel-Ulmer duality relating small bilex2-categories and finitely bipresentable 2-categories. Finally, we show that2-categories of pseudo-algebras of bifinitary pseudomonads on Cat are finitelybipresentable, which in particular captures the case of Lex, the 2-category ofsmall lex categories. Invoking the technology of lex-colimits, we prove furtherthat several 2-categories arising in categorical logic (Reg, Ex, Coh, Ext, Adh,Pretop) are also finitely bipresentable.

Bi-accessible and bipresentable 2-categories