To prepare an upcoming seminar talk I’m trying to find introductory texts on differential graded Hopf algebras (over a field $k$).
My knowledge of Hopf algebras encompasses roughly the first 5 chapters of Sweedler’s book. I also have a rough idea of how to define dg-Hopf algebras, namely by the same diagrams as an ordinary Hopf algebra but with dg-vector spaces instead of just vector spaces (i.e. as “Hopf objects” in the monoidal category of dg-vector spaces). I’m thus looking for references that do the following:
- Providing an explicit definition of dg-Hopf algebras and showing their fundamental properties.
- Giving (basic) examples for dg-Hopf algebras.
- Explaining the differences and similarities between ordinary Hopf-algebras and dg-Hopf algebras.
- (Giving me a way to check my thoughts and suspicions.)
I was originally given  and  as references (the last of which is also given on the nlab) but  only really deals with ordinary Hopf algebras and  doesn’t seem to provide introductory material. I already found , which provides some background on dg-algebras, -coalgebras and -Lie algebras, but only little on dg-bialgebras and nothing on dg-Hopf algebras.
: Loday, Cyclic Homology, Appendix A
: Quillen, Rational Homotopy Theory, Appendix B
: Félix, Halperin, Thomas, Rational Homotopy Theory, Chapters 3,21