# Definition:Hom Class

Jump to navigation
Jump to search

This article, or a section of it, needs explaining.In particular: A linguistic note explaining the source of the name -- it is not impossible that readers may be asking: "Who is the mathematician 'Hom' for whom this is named?" This note should be transcluded in all instances of "Hom" objects.You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by explaining it.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Explain}}` from the code. |

## Definition

Let $\mathbf C$ be a metacategory.

Let $C$ and $D$ be objects of $\mathbf C$.

The collection of morphisms $f: C \to D$ is called a **hom class** and is denoted $\operatorname{Hom}_{\mathbf C} \left({C, D}\right)$.

## Also known as

If $\operatorname{Hom}_{\mathbf C} \left({C, D}\right)$ is a set, then it is also called a **hom set**.

Some authors hyphenate, resulting in **hom-class** and **hom-set**.

## Also denoted as

When the category $\mathbf C$ is clear, it is mostly dropped from the notation, yielding $\operatorname{Hom} \left({C, D}\right)$.

The **hom class** is also denoted $\mathbf C \left({C, D}\right)$, or in the case of a functor category, $\operatorname{Nat}(C, D)$.

## Also see

## Sources

- 2010: Steve Awodey:
*Category Theory*(2nd ed.) ... (previous) ... (next): $\S 1.8$: Definition $1.12$ - 2010: Steve Awodey:
*Category Theory*(2nd ed.) ... (previous) ... (next): $\S 2.7$