• The n-Category Café Skip to the Main Content Note:These pages make extensive use of the latest XHTML and CSSStandards. • They ought to look great in any standards-compliant modern browser. • Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. • Moreover, many posts use MathML, which is, currentlyonlysupported in Mozilla. • My best suggestion (and you willthankme when surfing an ever-increasing number of sites on the web which have been crafted to use the new standards) is to upgrade to the latest version of your browser. • If that’s not possible, consider moving to the Standards-compliant and open-sourceMozillabrowser.
Article Summaries:
- Tom Leinster’s new paper “Equivalence via Surjections” (arXiv 2508.20555, 2025) introduces the notion of a strict surjective equivalence: an equivalence that is literally surjective on all levels and preserves structure strictly. He proves that for many categorical structures-bicategories, monoidal categories, double categories-any standard equivalence can be built from zigzags of such strict surjective equivalences. This principle clarifies the appropriate notion of equivalence for structures where it is unclear, notably providing a new justification for the “gregarious double equivalence” proposed by Campbell. The paper also discusses concrete examples, such as categories, where the theorem reduces to ordinary equivalence via surjective functors.
Sources: