Examples of 'functors' in a sentence
Meaning of "functors"
In mathematics, a functor is a mapping between categories. It is a way to associate to each object of one category another object of a different category
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- plural of functor
How to use "functors" in a sentence
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functors
Functors can be thought of as homomorphisms between categories.
Both of these functors have left adjoints.
Functors like these are called representable functors.
Identity of composition of functors is the identity functor.
A morphism of presheaves is defined to be a natural transformation of functors.
Contravariant functors are also occasionally called cofunctors.
Introduction to the theory of categories and functors.
Functors sometimes appear in functional programming.
It follows that adjoint functors induce homotopy equivalences.
Most functors studied between preadditive categories are additive.
Instances of such classes are called functors or function objects.
Forgetful functors are almost always faithful.
Functions between orders become functors between categories.
Left derived functors are zero on all projective objects.
Function objects are often called functors.
See also
These functors are called pushforwards.
Morphisms in this category are natural transformations between functors.
Almost all functors studied between additive categories are additive.
This concept is generalised by adjoint functors.
Note that contravariant functors reverse the direction of composition.
Elementary embeddings are natural transformations between these functors.
Functors require annotating arguments.
The terminology of completeness is often used in discussions of signalizer functors.
The next three functors enable reordering argument lists at will.
Universal constructions often give rise to pairs of adjoint functors.
Diagonal functors provide a way to define limits and colimits of diagrams.
For each comma category there are forgetful functors from it.
Functors for which this assumption does not hold are called intensional.
The coherence maps of strong monoidal functors are invertible.
Functors that preserve finite limits are often said to be left exact.
The operations are six functors.
We can also look at functors as things that output values in a context.
There is also a close relation to the concept of adjoint functors.
We have already talked about functors in their own little section.
But there also exists a natural notion of morphisms of functors.
They are given by functors which are compatible with the topology in a certain sense.
Let us see if this law holds for a few values of functors.
The concept of derived functors explains and clarifies many of these observations.
Programs are then denoted by natural continuous functions between these functors.
Exact functors are functors that transform exact sequences into exact sequences.
Properties of adjoint functors.
Smooth functors may therefore be uniquely extended to functors defined on vector bundles.
A small example of how one could use the functors is as follows.
Ordinary functors are also called covariant functors in order to distinguish them from contravariant ones.
Definition by derived functors.
The definitions of categories and functors provide only the very basics of categorical algebra.
The main problem is to prove a signalizer functor theorem for nonsolvable signalizer functors.
Diagrams as functors.
Category theory takes the idea of mathematical analogy much further with the concept of functors.
We have functors.
