45 citations · 402 across the 46 of their papers we have counts for
51 papers
Plethysm Products, Element and Plus Constructions
Ralph M. Kaufmann, Michael Monaco
Motivated by viewing categories as bimodule monoids over their isomorphism groupoids, we construct monoidal structures called plethysm products on three levels: that is for bimodul…
Plus constructions, plethysm, and unique factorization categories with applications to graphs and operad-like theories
Ralph M. Kaufmann, Michael Monaco
Baez-Dolan type plus constructions serve three main purposes: They (1) corepresent categorical bimodules that are monoids with respect to a plethysm product, (2) allow to define fu…
Trees, graphs and aggregates: a categorical perspective on combinatorial surface topology, geometry, and algebra
Clemens Berger, Ralph M. Kaufmann
Taking a Feynman categorical perspective, several key aspects of the geometry of surfaces are deduced from combinatorial constructions with graphs. This provides a direct route fro…
Koszul Feynman Categories
Ralph M. Kaufmann, Benjamin C. Ward
A cubical Feynman category, introduced by the authors in previous work, is a category whose functors to a base category behave like operads in . In this…
A combinatorial -algebra structure on cubical cochains and the Cartan-Serre map
Ralph M. Kaufmann, Anibal M. Medina-Mardones
Cubical cochains are equipped with an associative product, dual to the Serre diagonal, lifting the graded commutative structure in cohomology. In this work we introduce through exp…
Pathlike Co/Bialgebras and their Antipodes with Applications to Bi- and Hopf Algebras Appearing in Topology, Number Theory and Physics
Ralph M. Kaufmann, Yang Mo
We develop an algebraic theory of colored, semigrouplike-flavored and pathlike co-, bi- and Hopf algebras. This is the right framework in which to discuss antipodes for bialgebras…