Get to know Morphism better with 10+ real example sentences, the meaning.
Morphism meaning
- (formally) An arrow in a category; (less formally) an abstraction that generalises a map from one mathematical object to another and is structure-preserving in a way that depends on the branch of mathematics from which it arises.
- Being or having distinct variants of a plant or animal species in the same locale; polymorphism.
Using Morphism
- The main meaning on this page is: (formally) An arrow in a category; (less formally) an abstraction that generalises a map from one mathematical object to another and is structure-preserving in a way that depends on the branch of mathematics from which it arises. | Being or having distinct variants of a plant or animal species in the same locale; polymorphism.
- In the example corpus, morphism often appears in combinations such as: every morphism, morphism of, morphism from.
Context around Morphism
- Average sentence length in these examples: 24 words
- Position in the sentence: 9 start, 8 middle, 3 end
- Sentence types: 20 statements, 0 questions, 0 exclamations
Corpus analysis for Morphism
- In this selection, "morphism" usually appears near the start of the sentence. The average example has 24 words, and this corpus slice is mostly made up of statements.
- Around the word, zero, initial, covering, alone and occurs stand out and add context to how "morphism" is used.
- Recognizable usage signals include a c morphism e x and a covering morphism of groupoids. That gives this page its own corpus information beyond isolated example sentences.
- By corpus frequency, "morphism" sits close to words such as abated, aberrations and activations, which helps place it inside the broader word index.
Example types with morphism
The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:
Color morphism occurs in the species. (6 words)
A groupoid is a category in which every morphism is an isomorphism. (12 words)
A split epimorphism is a morphism which has a right-sided inverse. (12 words)
That is, if f: A → B is a morphism in a preadditive category, then the kernel of f is the equaliser of f and the zero morphism from A to B, while the cokernel of f is the coequaliser of f and this zero morphism. (45 words)
If D is a subcategory of C, then every morphism in D which is an epimorphism when considered as a morphism in C is also an epimorphism in D; the converse, however, need not hold; the smaller category can (and often will) have more epimorphisms. (45 words)
Any preordered set (P, ≤) forms a small category, where the objects are the members of P, the morphisms are arrows pointing from x to y when x ≤ y. Between any two objects there can be at most one morphism. (39 words)
Example sentences (20)
That is, if f: A → B is a morphism in a preadditive category, then the kernel of f is the equaliser of f and the zero morphism from A to B, while the cokernel of f is the coequaliser of f and this zero morphism.
Given a functor U and an object X as above, there may or may not exist an initial morphism from X to U. If, however, an initial morphism (A, φ) does exist then it is essentially unique.
If D is a subcategory of C, then every morphism in D which is an epimorphism when considered as a morphism in C is also an epimorphism in D; the converse, however, need not hold; the smaller category can (and often will) have more epimorphisms.
This action groupoid comes with a morphism which is a covering morphism of groupoids.
This means that every monomorphism is a kernel of some morphism, and every epimorphism is a cokernel of some morphism.
A fibration is called a covering morphism or covering of groupoids if further such an is unique.
A groupoid can be seen as a: * Group with a partial function replacing the binary operation ; * Category in which every morphism is invertible.
A groupoid is a category in which every morphism is an isomorphism.
Algebra In general, for an algebraic category C, an embedding between two C-algebraic structures X and Y is a C-morphism e:X→Y which is injective.
A morphism f:A → B of rings is a homological epimorphism if it is an epimorphism and it induces a full and faithfull functor on derived categories: D(f) : D(B) → D(A).
Any morphism with a right inverse is an epimorphism, but the converse is not true in general.
Any preordered set (P, ≤) forms a small category, where the objects are the members of P, the morphisms are arrows pointing from x to y when x ≤ y. Between any two objects there can be at most one morphism.
A split epimorphism is a morphism which has a right-sided inverse.
As some of the above examples show, the property of being an epimorphism is not determined by the morphism alone, but also by the category of context.
Briefly, if we consider a morphism between two objects as a "process taking us from one object to another", then higher-dimensional categories allow us to profitably generalize this by considering "higher-dimensional processes".
Color morphism A melanistic jaguar is a color morph which occurs at about 6 percent frequency in populations.
Color morphism occurs in the species.
Dually, a universal morphism from U to X is a terminal object in (U ↓ X).
Each morphism f has a source object a and a target object b where a and b are in ob(C).
Equivalent formulations The definition of a universal morphism can be rephrased in a variety of ways.
Common combinations with morphism
These word pairs occur most frequently in English texts:
- every morphism 8×
- morphism of 8×
- morphism from 7×
- morphism is 6×
- is morphism 5×
- morphism in 4×
- the morphism 4×
- universal morphism 4×
- initial morphism 3×
- zero morphism 2×