Talk:Sieve (disambiguation)

From Wikipedia, the free encyclopedia
Jump to: navigation, search
WikiProject Disambiguation
WikiProject icon This page is within the scope of WikiProject Disambiguation, an attempt to structure and organize all disambiguation pages on Wikipedia. If you wish to help, you can edit the page attached to this talk page, or visit the project page, where you can join the project and/or contribute to the discussion.

Category Theory[edit]

Is "sieve" indeed something in category theory to glue things together, or do you mean "sheaf"? Perhaps such elaborations don't belong in a disambiguation page and we should only refer as it as "Sieve (category theory)".

I am not an expert, but what I know is from [1]. A sieve S on an object a is a collection of arrows that ends in a (so, a is the codomain) and is "closed under composition on the right". The latter means that if there is an arrow (a morphism) from node b to a in the sieve, then for all arrows leading to b, there is a corresponding composed arrow in S. So, the sieve wraps all arrows leading b and connects it to a. There can be multiple sieves on an object. It depends on how many incoming arrows the object a has.

It is possible to define a sheaf using covering sieves. But like you would be able to get from above is that a sieve is not the one defining how to glue.

[1] "Pattern matching: a sheaf-theoretic approach", Srinivas, PhD thesis, 1991, University of California

Andy (talk) 03:49, 31 March 2010 (UTC)