sieves in nLab

["Vasili I. Galchin" <vigalchin@gmail.com>]

Hello,

      I am confused about the notion of "encoding" regarding sieves:



." And sieves on objects are mostly used in the context of
Grothendieck topologies to encode presheaves that behave like
coverings"


"Sieves are an equivalent way to encode subobjects of representable
functors in a presheaf category in terms of the total sets of elements
of such a subfunctor."

"It is in this way that sieves and their associated subfunctors encode
the notion of cover of an object V: they tell us which of all the maps
into V do factor through the cover."


Regards,

Vasili


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