Editing Grothendieck topology (section)

=== The discrete and indiscrete topologies ===

Let '''C''' be any category.  To define the '''discrete topology''', we declare all sieves to be covering sieves.  If '''C''' has all fibered products, this is equivalent to declaring all families to be covering families.  To define the '''indiscrete topology''', also known as the '''coarse''' or '''chaotic''' topology,<ref>[[Séminaire de Géométrie Algébrique du Bois Marie|SGA]] IV, II 1.1.4.</ref> we declare only the sieves of the form Hom(&minus;, ''X'') to be covering sieves.  The indiscrete topology is generated by the pretopology that has only isomorphisms for covering families. A sheaf on the indiscrete site is the same thing as a presheaf.