What is the translation of " FUNCTOR " in Chinese?

• 函子
• 一个functor

Examples of using Functor in English and their translations into Chinese

F*F^* is a functor.
其中，f是一个Functor。

A functor maps a category to another category.
Functor将一个category映射到另一个category。

Where F is a functor.
其中，f是一个Functor。

A functor which is both faithful and full is called fully faithful.
完全忠实函子：既完全且忠实的函子称为完全忠实函子。

Which defines a functor.
自定义一个Functor.

A functor from a category to itself is called an endofunctor.
如果一个Functor从一个范畴映射到自己，称为endofunctor。

Where the'f' is a functor.
其中，f是一个Functor。

A functor also maps morphisms, so it is a higher order function- fmap.
函子，也能将态射映射为态射，因此它也是高阶函数--fmap。

And satisfies the functor laws:.
显然，其满足了functor定律：.

The functor Reader() takes any type a and maps it into a function type()-gt;a.
函子Reader()接受任何一种类型a，将它射入函数类型()-gt;a。

So, the identity map is a functor.
所以map就是一个functor。

In Haskell, the action of a functor G on a morphism f is implemented using fmap.
在Haskell中，函子G作用于一个态射f是通过fmap实现的。

A functor F: C→ D yields an equivalence of categories if and only if it is simultaneously:.
可以证明函子F:C→D给出范畴的等价当且仅当它是：.

An object in Hask is a type, so our functor must map types into types.
Hask中的一个对象就是一个类型，因此我们的函子必须将类型映射为类型。

The functor category between categories C and D is written as Fun(C, D), or[C, D], or sometimes as DC.
范畴C与D之间的函子范畴记为Fun(C,D)或[C,D]，有时也写成D^C。

You might remember the example of a contravariant functor we have looked at before:.
你可能还记得之前我们见过的一个逆变函子的示例：.

The way to look at it is that a functor in Hask constructs one type from another- it's a type constructor.
这种方式看上去就像是Hask中的函子可以从一种类型构建出另一种类型--它就是一个类型构造子。

Now let's consider natural transformations from this functor to the Maybe functor:.
现在，来看一下从这种函子到Maybe函子的自然变换：.

Pluck will work on any functor in addition to arrays, as it is equivalent to R. map(R. prop(k), f).
Pluck可以作用于任何functor，包括Array，因为它等价于R.map(R.prop(k),f)。

For instance, length can be thought of as a natural transformation from the list functor to the Const Int functor:.
例如，可将length视为从列表函子到ConstInt函子的自然变换：.

How likely is it that it also defines a functor(loosely speaking- C++ is not as mathematized as Haskell)?
用它来定义一个函子怎么样？（不严格的说--C++不像Haskll那样数学化）。?

The list functor obviously preserves function composition and identity(I will leave it as an easy but instructive exercise for the reader).
列表函子显然保持了函数的复合性与单位性（这个要留给读者当作一个简单但有意义的课后作业）。

The quickest way to define a contravariant functor is as a covariant functor from the opposite category Cop to D.
定义反变函子的最简捷的方法是作为C的反范畴Cop到D上的函子。

Functors in Haskell are from Hask to func, where func is the subcategory of Hask defined on just that functor's types.
Haskell中的Functor其实是把Hask转换到Hask子范畴Func的函子，范畴Func是定义在该Functor的类型之上的一个范畴。

Unfortunately they can also be quite cumbersome to use, particularly if the functor you would like to apply is unique to the particular function.
不幸的是，它们的使用有时也很麻烦，特别是如果你想应用的函子是特定函数的唯一函子的话。

Finally, for each functor F there is an identity natural transformation 1F whose components are the identity morphisms:.
最后，对于每个函子F，存在一个恒等自然变换1_F，它的分量是恒等态射：.

This is not a functor because the same type a is used both in the negative(contravariant) and positive(covariant) position.
这不是一个函子，因为同一类型的a出现在负（逆变）位与正（协变）位上。

We can, however, re-interpret the functor arrow as a special kind of natural transformation: the identity natural transformation acting on this functor.
然而，我们可以将函子箭头重新解释为一种特殊的自然变换：恒等自然变换作用于这个函子。

Takes a function and a functor, applies the function to each of the functor's values, and returns a functor of the same shape.
接收一个函数和一个functor,将该函数应用到functor的每个值上，返回一个具有相同形态的functor。