monomorphism sentence in Hindi
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- Applying duality, this means that a morphism in some category " C " is a monomorphism if and only if the reverse morphism in the opposite category " C " op is an epimorphism.
- This means that a ( homo ) morphism f : A \ to B is a monomorphism if, for any pair of morphisms from any other object to, then f \ circ g = f \ circ h implies.
- In the category of vector spaces over a field " K ", every monomorphism and every epimorphism splits; this follows from the fact that linear maps can be uniquely defined by specifying their values on a basis.
- In particular, Mac Lane attempted to settle an ambiguity in usage for the terms epimorphism and monomorphism by introducing the terms " epic " and " monic, " but the distinction is not in common use.
- By dividing the two conditions on the induced map in the definition, one can define "'left semi-abelian categories "'by requiring that \ overline { f } is a monomorphism for each morphism f.
- Such a factorization of an arbitrary morphism into an epimorphism followed by a monomorphism can be carried out in all abelian categories and also in all the concrete categories mentioned above in the Examples section ( though not in all concrete categories ).
- As an example, the inclusion of the rational numbers into the real numbers is a monomorphism and an epimorphism, but it is clearly not an isomorphism; this example shows that "'Met "'is not a balanced category.
- Monomorphism is the ancestral state, and " X . micans ", which shows both mating strategies, have males partially covered in light hairs, showing the beginnings of sexual dimorphism that grows more prominent in species that require lek polygyny.
- Every morphism in a concrete category whose underlying function is injective is a monomorphism; in other words, if morphisms are actually functions between sets, then any morphism which is a one-to-one function will necessarily be a monomorphism in the categorical sense.
- Every morphism in a concrete category whose underlying function is injective is a monomorphism; in other words, if morphisms are actually functions between sets, then any morphism which is a one-to-one function will necessarily be a monomorphism in the categorical sense.
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