# Commit 2020-09-22 10:04 58d0bfcc

View on Github →feat(topology/sheaves): alternate formulation of the sheaf condition (#4190)
Currently the sheaf condition is stated as it often is in textbooks, e.g.
https://stacks.math.columbia.edu/tag/0072. That is, it is about an equalizer of the two maps `∏ F.obj (U i) ⟶ ∏ F.obj (U i) ⊓ (U j)`

.
This PR adds an equivalent formulation, saying that `F.obj (supr U)`

(with its natural projection maps) is the limit of the diagram consisting of the `F.obj (U i)`

and the `F.obj (U i ⊓ U j)`

.
I'd like to add further reformulations in subsequent PRs, in particular the nice one I saw in Lurie's SAG, just saying that `F.obj (supr U)`

is the limit over the diagram of all `F.obj V`

where `V`

is an open subset of *some* `U i`

. This version is actually much nicer to formalise, and I'm hoping we can translate over quite a lot of what we've already done about the sheaf condition to that version