Hom-Set

up:: Category

Given two objects $X,Y$, we say that the collection of all morphisms from $X$ to $Y$ is the collection $Hom(X,Y)$. That is,

$$Hom(X,Y):=\{X\stackrel{f}{\to }Y\}$$

Examples

• A Vector Space Dual is the Hom-Set $Hom(V,\mathbb{K})$ from a Vector Space $V$ to its Field $\mathbb{K}$.
• Between every object $X,Y$ inside a category $C$, there is a collection of morphisms $Hom(X,Y)$
• A category is said to be Locally Small Category when all of its Hom-Sets are, in fact, sets

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References

• Category (mathematics) - Wikipedia