Monoidal Functors, Species, and Hopf Algebras

By Marcelo Aguiar, Swapneel Mahajan. 2010

451 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/9e694f5bb676fe85d563d97244b747f02beb9366

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In Geometry and Topology

Citations in the corpus

Operadic categories and Duoidal Deligne's conjecture (2014, background): “The center has a natural structure of a duoid (double monoid in the terminology of [1]) in D .”
Admissibility and rectification of colored symmetric operads (2014, background): “Here η : 1[1] → O is the unit of O, which is the unique morphism of operads 1[1] → O.”
Skew-monoidal categories and bialgebroids (2012, background): “ze monoidal categories which also have non-invertible comparison cells but no associator in the ordinary ‘biased’ sense. Much closer in spirit to our approach is the 2-monoidal and duoidal categories [1, 5] of Aguiar and Mahajan in spite of that they use two ordinary monoidal structures instead of a”
Higher Dimensional Algebra VII: Groupoidification (2009, unknown): “Guta and Maassen [14] and Aguiar and Maharam [1] have also done relevant work.”
Hopf Algebras in Combinatorics (2014, background): “Furthermore, recent work of Ardila and Aguiar [3] has shown that there is a Hopf algebra of such generalized permutohedra, arising from a Hopf monoid in the sense of Aguiar and Mahajan [6].”
Combinatorial Topology and the Global Dimension of Algebras Arising in Combinatorics (2012, background): “Hyperplane face monoids also have a salient position in the work of Aguiar and Mahajan [3, 4] on combinatorial Hopf algebras.”
HOPF MONOIDS IN THE CATEGORY OF SPECIES (2012, background): “This important point was made in [5, 6, 54], and is discussed extensively here.”
Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras (2010, background): “parts that can also be put together with some compatibility between operations [24]. They have emerged as a central object of study in algebra through quantum groups [14, 18, 36] and in combinatorics [1, 4, 23]. Hopf algebras ﬁnd applications in diverse ﬁelds such as algebraic topology, representati”
Commutativity (2015, background): “These were introduced in a slightly degenerate form in [2] under the name 2-fold monoidal categories; the fully general definition may be found, for example, in [1] under the name 2-monoidal category.”
Hopf Monoids and Generalized Permutahedra (2017, background): “ota [48], Schmitt [67], Stanley [76] and others taught us that to study combinatorial objects, it is often useful to endow them with algebraic structures. Aguiar and Mahajan’s Hopf monoids in species [2] provide a particularly useful framework to study many important combinatorial families. Edmonds ”