nForum - Discussion Feed (coinvariant) 2020-05-30T20:33:21-04:00 https://nforum.ncatlab.org/ Lussumo Vanilla & Feed Publisher Urs comments on "coinvariant" (43268) https://nforum.ncatlab.org/discussion/5451/?Focus=43268#Comment_43268 2013-11-15T20:10:51-05:00 2020-05-30T20:33:21-04:00 Urs https://nforum.ncatlab.org/account/4/ So the coinvariant should just be the dependent sum, where the invariants is the dependent poduct. In this sense: for GG a group object, types VV with GG-action &rho; V\rho_V are ...

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 $\underset{\mathbf{B}G}{\sum} \rho_V \simeq V//G$.

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David_Corfield comments on "coinvariant" (43267) https://nforum.ncatlab.org/discussion/5451/?Focus=43267#Comment_43267 2013-11-15T19:48:12-05:00 2020-05-30T20:33:21-04:00 David_Corfield https://nforum.ncatlab.org/account/20/ Is there a HoTT formulation as for invariants?

Is there a HoTT formulation as for invariants?

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Urs comments on "coinvariant" (43242) https://nforum.ncatlab.org/discussion/5451/?Focus=43242#Comment_43242 2013-11-15T10:03:38-05:00 2020-05-30T20:33:21-04:00 Urs https://nforum.ncatlab.org/account/4/ 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 ...

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.

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