The category of superalmiares

Plática dada por Vladimir Vega (University of Miami y Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, CINVESTAV) en el evento Algebraic Geometry in 2016 el miércoles 1 de noviembre del 2016.

In this talk a functorial approach to define differentiable stacks is introduced. This approximation shows significative practical advantages respect to another theoretical frameworks based on the theory of descent and fibered categories since much of the involved structures are codified in some lifting properties of certain categories of presheaves.
The first results derived from this ideas are that the category of Lie groupoids is equivalent to certain category of presheaves with a lifting property and that strong Morita equivalence between Lie groupoids is translated in a natural isomorphism between such functors. The last statement permit us to construct a quotient category called the category of almiares which turn out be equivalent to the category of differentiable stacks.
Using similar arguments we extended the previous results to Lie super groupoids to construct the category of super almiares and finally the definition of super orbifold arises almost naturally.

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