Last Updated
：2025/11/27
presheaf
Noun
(category
theory,
algebraic
geometry)
A
contravariant
functor
whose
domain
is
a
category
whose
objects
are
open
sets
of
a
topological
space
and
whose
morphisms
are
inclusion
mappings.
The
functorial
images
of
the
open
sets
are
sets
of
things
called
sections
which
are
said
to
be
"over"
those
open
sets.
The
(contravariant)
functorial
images
of
those
inclusion
mappings
are
functions
which
are
called
restrictions.
Japanese Meaning
前層：トポロジー空間の開集合を対象、その包含写像を射とする圏からの反変関手として定義される。各開集合に対して、その関手はその集合上の断面（セクション）と呼ばれる要素集合を割り当て、包含写像に対応して制限写像（リストリクション）を与える。
Sense（1）
(category
theory,
algebraic
geometry)
A
contravariant
functor
whose
domain
is
a
category
whose
objects
are
open
sets
of
a
topological
space
and
whose
morphisms
are
inclusion
mappings.
The
functorial
images
of
the
open
sets
are
sets
of
things
called
sections
which
are
said
to
be
"over"
those
open
sets.
The
(contravariant)
functorial
images
of
those
inclusion
mappings
are
functions
which
are
called
restrictions.
（ plural ）
Quizzes for review
(category theory, algebraic geometry) A contravariant functor whose domain is a category whose objects are open sets of a topological space and whose morphisms are inclusion mappings. The functorial images of the open sets are sets of things called sections which are said to be over
those open sets. The (contravariant) functorial images of those inclusion mappings are functions which are called restrictions.
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See correct answer
presheaf
On the topological space X, the presheaf assigns to each open set a set of sections and provides restriction maps for inclusions.
See correct answer
On the topological space X, the presheaf assigns to each open set a set of sections and provides restriction maps for inclusions.
音声機能が動作しない場合はこちらをご確認ください
English - English
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