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Orthogonal group and adjoints

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HHH - Homotopy harnessing higher structures

In
this talk I will articulate and contextualize the following sequence of results.

The
Bruhat decomposition of the general linear group defines a stratification
of the orthogonal group.Matrix
multiplication defines an algebra structure on its exit-path category in a
certain Morita category of categories.  In
this Morita category, this algebra acts on the category of
n-categories —this action is given by adjoining adjoints to
n-categories. 

This result is extracted from a
larger program—entirely joint with John Francis, some parts joint with Nick
Rozenblyum—which proves the cobordism hypothesis.  

This talk is part of the Isaac Newton Institute Seminar Series series.

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