sieves in nLab

sieves in nLab

[Vasili I. Galchin]

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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Re: sieves in nLab

[Toby Bartels]

Vasili I. Galchin wrote in part on the categories list:

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

Looking through the history of the page,
it seems that Urs Schreiber introduced that term.
So he might be able to say what he meant by it.
(I'm pretty sure that he reads this list,
  but I'll Cc him to be safe.)

By the way, the page is http://ncatlab.org/nlab/show/sieve
for anybody who doesn't know how to find it.


--Toby


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Re: sieves in nLab

[Urs Schreiber]

Dear Vasili;

concerning the nLab entry "sieve"

   http://ncatlab.org/nlab/show/sieve

you had written

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

It seems that I had once used this word in an attempt to express the
fact that  while the notions of "sieve" (on an object) and
"subfunctor" (of the functor represented by that object) are not
_identitcal_ notions, one does determine ("encode") the other. Sorry
if that wasn't a good formulation. Finn Lawler has meanwhile been so
kind to improve the phrasing a bit.

By the way, questions and comments about nLab pages are mostly best
sent to the community of people who work on that wiki and these people
can jointly be contacted by posting a message to the "nForum".

There is now for instance a thread discussing your question, which you
can see here:

http://www.math.ntnu.no/~stacey/Mathforge/nForum/comments.php?DiscussionID=2534&page=1

All the best,
Urs


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