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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We extend the basic concepts of Street's formal theory of monads from thesetting of 2-categories to that of double categories. In particular, weintroduce the double category Mnd(C) of monads in a double category C anddefine what it means for a double category to admit the construction of freemonads. Our main theorem shows that, under some mild conditions, a doublecategory that is a framed bicategory admits the construction of free monads ifits horizontal 2-category does. We apply this result to obtain doubleadjunctions which extend the adjunction between graphs and categories and theadjunction between polynomial endofunctors and polynomial monads.

Monads in Double Categories