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

Tannaka Duality describes the relationship between algebraic objects in agiven category and their representations; an important case is that of Hopfalgebras and their categories of representations; these have strong monoidalforgetful "fibre functors" to the category of vector spaces. We simultaneouslygeneralize the theory of Tannaka duality in two ways: first, we replace Hopfalgebras with weak Hopf algebras and strong monoidal functors with separableFrobenius monoidal functors; second, we replace the category of vector spaceswith an arbitrary braided monoidal category. To accomplish this goal, weintroduce a new graphical notation for functors between monoidal categories,using string diagrams with coloured regions. Not only does this notation extendour capacity to give simple proofs of complicated calculations, it makes plainsome of the connections between Frobenius monoidal or separable Frobeniusmonoidal functors and the topology of the axioms defining certain algebraicstructures. Finally, having generalized Tannaka to an arbitrary base category,we briefly discuss the functoriality of the construction as this base isvaried.

Graphical Methods for Tannaka Duality of Weak Bialgebras and Weak Hopf Algebras in Arbitrary Braided Monoidal Categories