[[!redirects H-magmoids]] ## Contents ## * table of contents {:toc} ## Definition ## An H-magmoid $A$ consists of the following. * A type $A_0$, whose elements are called objects. Typically $A$ is coerced to $A_0$ in order to write $x:A$ for $x:A_0$. * For each $a,b:A$, a type $hom_A(a,b)$, whose elements are called **arrows** or **morphisms**. * For each $a,b,c:A$, a function $$hom_A(b,c) \to hom_A(a,b) \to hom_A(a,c)$$ called composition, and denoted infix by $g \mapsto f \mapsto g \circ f$, or sometimes $gf$. ## See also ## * [[quiver]] * [[H-spaceoid]] * [[homotopy precategory]]