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1 - Grothendieck topologies and applicationsJournal of Linear and Topological Algebra , Issue 2 , Year , Spring 2023Following [6], we define Grothendieck topologies on a small category and describe sheaves for these Grothendieck topologies. This generalizes, in a natural way, the theory of sheaves on a topological spaceFollowing [6], we define Grothendieck topologies on a small category and describe sheaves for these Grothendieck topologies. This generalizes, in a natural way, the theory of sheaves on a topological space Manuscript profile