$k$-theory algebraictopology associativeringsandalgebras braidedcategories categorieswithstructure categorytheory;homologicalalgebra grouptheoryandgeneralizations higheralgebraic$k$-theory hopfalgebras hopfalgebrasandtheirapplications liealgebrasandliesuperalgebras linearalgebraicgroupsandrelatedtopics monoidalcategories(=multiplicativecategories) nonassociativeringsandalgebras quantumgroups(quantizedenvelopingalgebras)andrelateddeformations quantumgroups(quantizedfunctionalgebras)andtheirrepresentations quantumgroupsandrelatedtopics symmetricmonoidalcategories tensorfields