**Data**

- Title: The web algebra
- Authors: Marco Mackaay, Weiwei Pan and Daniel Tubbenhauer
- Status: Math. Z. 277-1-2 (2014), 401-479. Last update: Sat, 10 Mar 2018 12:15:16 GMT
- ArXiv link: http://arxiv.org/abs/1206.2118
- ArXiv version = 0.99 published version
- LaTex Beamer presentation: Slides1

**Abstract**

**A few extra words**

- If and are different, then, by convention, the multiplication is zero.
- If , then glue the foams together via a multiplication foam.
- The multiplication foam is made of saddles (arc-split), unzips (Y-split) and square removals (H-split). The picture shows a saddle and an unzip.
- The picture below is one part of the proof that the multiplication does not depend on the isotopy type. Note that the part of the foams corresponding to and is not shown, since it will be the identity.
- Note that one can speak of a categorification, i.e. on web level the multiplication is trivial (erase the middle and glue top and bottom), but on foam level lots of interesting mathematics is happening.