MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Thanks for pointing out any reference.

share|cite|improve this question
Is there a specific setting in which you want to study homotopy (co)invariants? For example, do you have in mind a question about topological spaces, or complexes of vector spaces? Are you looking for an abstract homotopy-theoretic treatment? – S. Carnahan Nov 1 '10 at 16:39
In Costello's work "The Gromov-Witten potential associated to a TCFT", it says the pullback operation is not well-defined in simplicial chain, but it is defined for homotopy coinvariant, that's what I am studying. – HYYY Nov 14 '10 at 9:52

If you like complexes of vector spaces over the field with two elements, Lecture 2 in this set of notes by Jacob Lurie has a nice treatment of homotopy coinvariants in that context. Some technical complexity that arises in the topological category is avoided in the linear algebraic treatment.

share|cite|improve this answer
Analogues of coinvariants for comodule algebras over Hopf algebras in model categorical setup is in a recent paper of Kathryn Hess on the arXiv. – Zoran Skoda Nov 1 '10 at 9:38

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.