Perverse Schobers

The notion of a perverse sheaf, introduced in [BBD], has come to play a central role in algebraic geometry and representation theory. In particular, appropriate categories of perverse sheaves provide “categorifications” of various representation spaces, these spaces being recovered as the Grothedieck groups of the categories. The goal of this paper is to suggest the possibility of categorifying the very concept of a perverse sheaf. In other words, we propose to develop a theory of perverse sheaves not of vector spaces but of triangulated categories.

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