We study Hopf monoids in entropic semi-additive varieties with an emphasis on adjunctions related to the enveloping monoid functor and the primitive element functor. These investigations are based on the concept of the abelian core of a semi-additive variety variety and its monoidal structure in case the variety is entropic.Comment: 13 pages

@article{Porst17,
  title = {Hopf and Lie algebras in semi-additive Varieties},
  author = {Hans-E. Porst},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 13, Issue 2},
  number = {Coalgebraic methods},
  year = {2017},
  doi = {10.23638/lmcs-13(2:3)2017}
}