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Homology of monoids with coefficients in group completion

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The group completion of a monoid gives a left adjoint to the inclusion of the category of groups into monoids. The Janelidze Galois structure for this adjunction has been worked out, unfortunately the general theory that gives higher Hopf formulae for the corresponding homology doesn’t apply to this setting. I’ve been working on determining a Hopf-type formula for this homology using a different approach, based on a proof of Hopf’s formula for group homology using crossed modules.

This talk is part of the Category Theory Seminar series.

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