English Dictionary

natural transformation

名詞

(category theory) A morphism between a pair of parallel functors such that if each object of the shared domain category subtends a correlated arrow — called a component — in the shared codomain (which arrow represents the difference between applying the second functor and the first functor to the correlated object) then each arrow of the shared domain subtends a commuting square — called a naturality square — between two components (correlated to the domain and codomain of the arrow).

日本語の意味

圏論において、二つの平行な関手の間の射（自然変換）を意味する。具体的には、ある圏から二つの関手が与えられたとき、各対象に対して対応する射（成分）を割り当て、その対応が射に関して自然性条件、すなわち各射に対応する自然性正方形が可換になるという性質を持つ変換を指す。

To prove the equivalence of the two functors, she constructed a natural transformation whose components assign to each object a morphism and whose naturality squares commute for every arrow in the domain.

二つの函手が同値であることを示すために、彼女は各対象に成分射を割り当て、定義域の任意の射に対して対応する成分の間で可換な自然性の方形（自然性の図式）を生じさせる、平行な函手間の写像である自然変換を構成した。

意味（1）

(category theory) A morphism between a pair of parallel functors such that if each object of the shared domain category subtends a correlated arrow — called a component — in the shared codomain (which arrow represents the difference between applying the second functor and the first functor to the correlated object) then each arrow of the shared domain subtends a commuting square — called a naturality square — between two components (correlated to the domain and codomain of the arrow).

natural transformations （ plural ）