[[Category theory MOC]]
# Oidification

Given some kind algebraic structure, say a gadget, a **gadgetoid** is a kind of _typed_ or _partial_ gadget, i.e. a [[category]]-like structure[^magmoid] such that a gadget is a single-object gadgetoid.
The elements of a gadget become the arrows of a gadgetoid.
Thus the process of **oidification**, also called **horizontal categorification**, is a kind of [[Split epimorphism|section]] to the process of specializing to a single object.

  [^magmoid]: By category-like structure, I really mean some kind of [[magmoid]].

This is one of two broad approaches for turning something into a category. See also (vertical) [[Categorification]].

## Examples

| Gadget                | Gadgetoid    |
| --------------------- | ------------ |
| [[Magma]]             | [[Magmoid]]  |
| [[Monoid]]            | [[Category]] |
| [[Group]]             | [[Groupoid]] |
| [[Set]]               | [[Quiver]]   |
| [[Monoidal category]] | [[Bicategory]]             |

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