$k$-theory 16t0516t1016s4016t3017b3517b3718d1018c1519a22 algebrasforatriple associativeringsandalgebras bialgebras braidedcategories burnsideandrepresentationrings categoriesandtheories categorieswithstructure categorytheory;homologicalalgebra congresses connectionswithcombinatorics frobeniusinduction grothendieckgroupsand$k_0$ homologyandderivedfunctorsfortriples hopfalgebras hopfalgebrasandtheirapplications liealgebrasandliesuperalgebras monadortriad) monoidalcategories(=multiplicativecategories) nonassociativeringsandalgebras quantumgroups(quantizedenvelopingalgebras)andrelateddeformations quantumgroupsandrelatedtopics ringsandalgebrasarisingundervariousconstructions smashproductsofgeneralhopfactions symmetricmonoidalcategories triples(=standardconstruction