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

Poly-bicategories generalise planar polycategories in the same way asbicategories generalise monoidal categories. In a poly-bicategory, theexistence of enough 2-cells satisfying certain universal properties(representability) induces coherent algebraic structure on the 2-graph ofsingle-input, single-output 2-cells. A special case of this theory was used byHermida to produce a proof of strictification for bicategories. No fullstrictification is possible for higher-dimensional categories, seemingly due toproblems with 2-cells that have degenerate boundaries; it was conjectured by C.Simpson that semi-strictification excluding units may be possible.  We study poly-bicategories where 2-cells with degenerate boundaries arebarred, and show that we can recover the structure of a bicategory through adifferent construction of weak units. We prove that the existence of theseunits is equivalent to the existence of 1-cells satisfying lower-dimensionaluniversal properties, and study the relation between preservation of units anduniversal cells.  Then, we introduce merge-bicategories, a variant of poly-bicategories withmore composition operations, which admits a natural monoidal closed structure,giving access to higher morphisms. We derive equivalences between morphisms,transformations, and modifications of representable merge-bicategories and thecorresponding notions for bicategories. Finally, we prove asemi-strictification theorem for representable merge-bicategories with a choiceof composites and units.

Weak units, universal cells, and coherence via universality for bicategories