Abstract
In [Cvetko-Vah, Non-commutative frames, J. Algebra Appl. (2018), https://doi.org/10.1142/S0219498819500117 ] noncommutative frames were introduced, generalizing the usual notion of frames of open sets of a topological space. In this paper, we extend this notion to noncommutative versions of Grothendieck topologies and their associated noncommutative toposes of sheaves of sets.
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