Definitionen
1.NounA quantity of the stalks and ears of wheat, rye, or other grain, bound together; a bundle of grain or straw.
2.NounAny collection of things bound together."a sheaf of paper"
3.NounA bundle of arrows sufficient to fill a quiver, or the allowance of each archer.
4.NounA quantity of arrows, usually twenty-four.
5.NounA sheave.
6.NounAn abstract construct in topology that associates data to the open sets of a topological space (i.e. a presheaf) in such a way so as to make the local and global data compatible, generalizing the situation of functions, fiber bundles, manifold structure, etc. on a topological space. Formally, a presheaf
F
{\displaystyle {\mathcal {F}}}
whose sections are, in a technical sense, uniquely determined by their restrictions onto smaller sets: that is, given an open cover
{
U
i
}
{\displaystyle \{U_{i}\}}
of
U
{\displaystyle U}
:
If two sections over
U
{\displaystyle U}
agree under restriction to every
U
i
{\displaystyle U_{i}}
, then the sections are the same.
Given a family of sections
s
i
∈
F
(
U
i
)
{\displaystyle s_{i}\in {\mathcal {F}}(U_{i})}
such that all pairs
(
s
i
,
s
j
)
{\displaystyle (s_{i},s_{j})}
agree under restriction to
U
i
∩
U
j
{\displaystyle U_{i}\cap U_{j}}
, there is a (unique) section
s
{\displaystyle s}
over
U
{\displaystyle U}
whose restriction to
U
i
{\displaystyle U_{i}}
is
s
i
{\displaystyle s_{i}}
.
7.NounIf two sections over
U
{\displaystyle U}
agree under restriction to every
U
i
{\displaystyle U_{i}}
, then the sections are the same.
8.NounGiven a family of sections
s
i
∈
F
(
U
i
)
{\displaystyle s_{i}\in {\mathcal {F}}(U_{i})}
such that all pairs
(
s
i
,
s
j
)
{\displaystyle (s_{i},s_{j})}
agree under restriction to
U
i
∩
U
j
{\displaystyle U_{i}\cap U_{j}}
, there is a (unique) section
s
{\displaystyle s}
over
U
{\displaystyle U}
whose restriction to
U
i
{\displaystyle U_{i}}
is
s
i
{\displaystyle s_{i}}
.
9.VerbTo gather and bind into a sheaf; to make into sheaves"to sheaf wheat"
10.VerbTo collect and bind cut grain, or the like; to make sheaves.