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Speaker:
João Nuno Mestre
Datum:
Don, 22/11/2018 - 10:30 - 12:30
Location:
MPIM Seminar Room
Parent event:
Learning seminar on deformation theory In this talk we will see that the functor $C^*$ from dgLa to cdga admits a right adjoint up to homotopy $D$. In order to understand $D$, we will use the free-forgetful adjunction between dgLa and chain complexes: We will see that up to homotopy, $C^*$ composed with the free functor $F$ has a particularly simple form, which in the following week will let us write a simple expression for $D$ (up to homotopy, when computed on certain nice enough algebras).
The talk will include a discussion on some basics of $\infty$-categories used to prove the existence of $D$ - we'll mostly discuss homotopy pullbacks, computing some mapping spaces, and how to detect whether certain objects are homotopy limits.
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