Noun
Grothendieck topology (plural Grothendieck topologies)
(category theory) A structure on a category which makes the category's objects act like the open sets of a topological space.
Grothendieck also saw how to phrase the definition of covering abstractly; this is where the definition of a Grothendieck topology comes from. Source: Internet
Sites and sheaves seeAlso Let C be a category and let J be a Grothendieck topology on C. The pair (C, J) is called a site. Source: Internet