[[Abstract algebra MOC]]
# Magmoid

A **magmoid**[^aka] is the [[oidification]] of a [[magma]].
A (small) magmoid $\mathscr{M}$ consists of #m/def/algebra 

- a set of objects $\Ob(\mathscr M)$
- for every pair of objects $X,Y \in \Ob(\mathscr M)$ a set of arrows $\mathscr M(X,Y)$
- an operation $(\odot)$ so that given $\alpha \in \mathscr M(X,Y)$ and $\beta \in \mathscr M(Y,Z)$ we have $\beta \odot \alpha \in \mathscr M(X,Z)$

  [^aka]: Also **partial magma**

See [[Magmoid homomorphism]] and [[Category of magmoids]].

## Examples

- [[Continuous path#Algebra|Topological path algebra]]

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#state/tidy | #lang/en | #SemBr