Samenvatting
In this master’s thesis, we pursue higher stacks. We are motivated by curiosity, the deformation theory of presheaves of algebras and the deformation theory of abelian categories,whose origins are linked with the Hochschild complex and Ext-groups. In both these cases,
(pre)stacks help us to construct the right setting or enable us to make a geometric model.
In the case of presheaves of algebras, we need to consider deformations in the 2-categorical
setting of prestacks in order to fully obtain the link with the standard Hochschild deformation theory, extending the case of algebras. In the case of abelian categories, we obtain
the Hochschild complex of a linear category as the cotangent complex of a moduli space.
Higher stacks make a fruitful geometric model for this. The project is also an exploration in
the necessary background on model categories and ∞-categories to understand these higher
categorical settings.
| Datum prijs | 30 jun. 2022 |
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| Originele taal | English |