Grothendieck topologies and applications

Subject Areas : Category theory, homological algebra

K. Azi ¹ , H. Hamraoui ² , N. Haddar ³

1 - TAG Laboratory, Faculty of sciences, A\"{\i}n Chock Hassan II University, B.P 5366 Maarif, Casablanca, Morocco
2 - TAG Laboratory, Faculty of sciences, A\"{\i}n Chock Hassan II University, B.P 5366 Maarif, Casablanca, Morocco
3 - TAG Laboratory, Faculty of sciences, A\"{\i}n Chock Hassan II University, B.P 5366 Maarif, Casablanca, Morocco

Received: 2023-05-21 Accepted : 2023-06-29 Published : 2023-06-01

Keywords: Presheaves, sheaves, Grothendieck topology, topos, Zariski topology, Etale topology, Nisnevich topology,

Abstract :

Following [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

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