Spahn Ad(K)

Let KK be a 22-category, then adjunction \dashv is a relation on K 1K_1 (the 11-cells of KK). The relation is linear and composition makes K 1K_1 into a pomagma Ad(K)Ad(K) whose object set is K 1K_1 and hom(l,r)=(lr)hom(l,r)=(l\dashv r) if lrl\dashv r and empty otherwise.

We can also consider Ad(K)Ad(K) as a “22-twisted 22-category” where we have 22-morphisms between antiparallel 11-cells and whose level 22 is thin.

\dashv satisfies

if(lrs)then(rlrs)and(lrsr)if\;(l\dashv r\dashv s)\; then\; (rl\dashv rs)\;and\;(lr\dashv sr)

Created on December 9, 2012 at 16:45:59. See the history of this page for a list of all contributions to it.