Monoidal categories Graded vector spaces Monoidal functors Operad Lax monoidal functors Bilax monoidal functors in homological algebra 2-monoidal categories Higher monoidal categories Hopf monoids in species Monoidal structures on species Deformations of Hopf monoids The Coxeter complex of type $A$ Universal constructions of Hopf monoids Hopf monoids from geometry Hopf monoids from combinatorics Hopf monoids in colored species Fock functors From species to graded vector spaces Deformations of Fock functors From Hopf monoids to Hopf algebras: Examples Adjoints of the Fock functors Decorated Fock functors and creation-annihilation Colored Fock functors Appendices Categorical preliminaries Operads Pseudomonoids and the looping principle Monoids and the simplicial category