Yesterday we gave a brief and abstract description of Galois descent, the punchline of which was that Galois descent could abstractly be described as a natural equivalence… 1,352 more words

## Tags » Cohomology

#### Projective representations are homotopy fixed points

Yesterday we described how a (finite-dimensional) projective representation of a group functorially gives rise to a -linear action of on such that the Schur class classifies this action. 870 more words

#### Projective representations give categorical representations

Today we’ll resolve half the puzzle of why the cohomology group appears both when classifying projective representations of a group over a field and when classifying -linear actions of on the category of -vector spaces by describing a functor from the former to the latter. 898 more words

#### Projective representations

Three days ago we stated the following puzzle: we can compute that isomorphism classes of -linear actions of a group on the category of vector spaces over a field correspond to elements of the cohomology group… 662 more words

#### Fixed points of group actions on categories

Previously we described what it means for a group to act on a category (although we needed to slightly correct our initial definition). Today, as the next step in our attempt to understand… 1,318 more words

#### Group actions on categories

Yesterday we decided that it might be interesting to describe various categories as “fixed points” of Galois actions on various other categories, whatever that means: for example, perhaps real Lie algebras are the “fixed points” of a Galois action on complex Lie algebras. 752 more words

#### Sullivan Models

The concept of minimal model in rational homotopy theory was created by Dennis Sullivan in the 1960’s. He discovered in the category of topological spaces, that simply connected spaces can be… 1,274 more words