Matteo Tommasini

We fix any bicategory A together with a class of morphisms , such that there is a bicategory of fractions (as described by D. Pronk). Given another such pair and any pseudofunctor , we find necessary and sufficient conditions in order to have an induced pseudofunctor . Moreover, we give a simple description of in the case when the class is “right s...

We give a definition of atlases for ineffective orbifolds, and prove that this definition leads to the same notion of orbifold as that defined via topological groupoids.

In this paper we investigate the construction of bicategories of fractions originally described by D. Pronk: given any bicategory $C$ together with a suitable class of morphisms $W$, one can construct a bicategory $C[W^{-1}]$, where all the morphisms of $W$ are turned into internal equivalences, and that is universal with respect to this property....

We fix any pair (C,W) consisting of a bicategory and a class of morphisms in it, admitting a bicalculus of fractions, i.e. a "localization" of C with respect to the class W. In the resulting bicategory of fractions, we identify necessary and sufficient conditions for the existence of weak fiber products.

We fix any bicategory A together with a class of morphisms W_A, such that there is a bicategory of fractions A[W_A^{-1}]. Given another such pair (B,W_B) and any pseudofunctor F: A→B, we find necessary and sufficient conditions in order to have an induced equivalence of bicategories from A[W_A^{-1}] to B[W_B^{-1}]. In particular, this gives necessa...

We fix any bicategory A together with a class of morphisms W_A, such that there is a bicategory of fractions A[W_A^{-1}]. Given another such pair (B,W_B) and any pseudofunctor F: A→B, we find necessary and sufficient conditions in order to have an induced pseudofunctor G: A[W_A^{-1}]→B[W_B^{-1}]. Moreover, we give a simple description of G in the c...

We describe a bicategory (Red Orb) of reduced orbifolds in the framework of differential geometry (i.e. without any explicit reference to notions of Lie groupoids or differentiable stacks, but only using orbifold atlases, local lifts and changes of charts). In order to construct such a bicategory, we first define a 2-category (Red Atl) whose object...

We prove a result of cohomology and base change for families of coherent systems over a curve. We use that in order to prove the existence of (non-split, non-degenerate) universal families of extensions for families of coherent systems (in the spirit of the paper "Universal families of extensions" by H. Lange). Such results will be applied in subse...

We define a 2-category structure (Pre-Orb) on the category of reduced complex orbifold atlases. We construct a 2-functor F from (Pre-Orb) to the 2-category (Grp) of proper \'etale effective groupoid objects over the complex manifolds. Both on (Pre-Orb) and (Grp) there are natural equivalence relations on objects: (a natural extension of) equivalenc...