Explore Epimorphisms through 10+ example sentences from English, with an explanation of the meaning. Ideal for language learners, writers and word enthusiasts.
Epimorphisms meaning
plural of epimorphism
Using Epimorphisms
- The main meaning on this page is: plural of epimorphism
- In the example corpus, epimorphisms often appears in combinations such as: epimorphisms in, the epimorphisms, of epimorphisms.
Context around Epimorphisms
- Average sentence length in these examples: 21.6 words
- Position in the sentence: 0 start, 7 middle, 4 end
- Sentence types: 11 statements, 0 questions, 0 exclamations
Corpus analysis for Epimorphisms
- In this selection, "epimorphisms" usually appears in the middle of the sentence. The average example has 21.6 words, and this corpus slice is mostly made up of statements.
- Around the word, regular, ordinary, strong, behave and fail stand out and add context to how "epimorphisms" is used.
- Recognizable usage signals include all the epimorphisms of rings and backs of epimorphisms and push. That gives this page its own corpus information beyond isolated example sentences.
- By corpus frequency, "epimorphisms" sits close to words such as aadi, aayush and abbottabad, which helps place it inside the broader word index.
Example types with epimorphisms
The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:
However, they are exactly the same as the strong epimorphisms. (10 words)
It is very difficult, for example, to classify all the epimorphisms of rings. (13 words)
However, surjective ring homomorphisms are vastly different from epimorphisms in the category of rings. (14 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)
Saunders Mac Lane attempted to create a distinction between epimorphisms, which were maps in a concrete category whose underlying set maps were surjective, and epic morphisms, which are epimorphisms in the modern sense. (33 words)
Properties of the category of sets The epimorphisms in Set are the surjective maps, the monomorphisms are the injective maps, and the isomorphisms are the bijective maps. (27 words)
Example sentences (11)
Saunders Mac Lane attempted to create a distinction between epimorphisms, which were maps in a concrete category whose underlying set maps were surjective, and epic morphisms, which are epimorphisms in the modern sense.
Unfortunately this is incorrect; strong or regular epimorphisms behave much more closely to surjections than ordinary epimorphisms.
However, surjective ring homomorphisms are vastly different from epimorphisms in the category of rings.
However there are also many concrete categories of interest where epimorphisms fail to be surjective.
However, they are exactly the same as the strong epimorphisms.
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.
It is a common mistake to believe that epimorphisms are either identical to surjections or that they are a better concept.
It is very difficult, for example, to classify all the epimorphisms of rings.
Properties of the category of sets The epimorphisms in Set are the surjective maps, the monomorphisms are the injective maps, and the isomorphisms are the bijective maps.
This occurs if and only if C is closed under pull-backs of epimorphisms and push-outs of monomorphisms.
While this is not exactly true for monic maps, it is very close, so this has caused little trouble, unlike the case of epimorphisms.
Common combinations with epimorphisms
These word pairs occur most frequently in English texts:
- epimorphisms in 3×
- the epimorphisms 2×
- of epimorphisms 2×