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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeNov 15th 2013
• (edited Nov 15th 2013)

I noticed by accident that we have an entry coinvariant. Then I noticed that we also have an entry homotopy coinvariant functor.

I have now added cross-links between these entries and with invariant and orbit, so that they no longer remain hidden.

I also edited the first case of group representation coinvariants at coinvariant a little.

• CommentRowNumber2.
• CommentAuthorDavid_Corfield
• CommentTimeNov 15th 2013
• (edited Nov 15th 2013)

Is there a HoTT formulation as for invariants?

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeNov 15th 2013

So the coinvariant should just be the dependent sum, where the invariants is the dependent poduct.

In this sense: for $G$ a group object, types $V$ with $G$-action $\rho_V$ are $\mathbf{B}G$-dependent types.

The homotopy invariants are $\underset{\mathbf{B}G}{\prod} \rho_V \simeq H_{Grp}(G,V)$.

The homotopy co-invariants are $\underset{\mathbf{B}G}{\sum} \rho_V \simeq V//G$.