كائن ماغما

في الرياضيات ، يمكننا تعريف كائن ماغمي Magma object أو ماغما ضمن تصنيف magma in a category ضمن تصنيف رياضي ${\displaystyle{\displaystyle\mathbf{C}}}$ equipped with a distinguished bifunctor ${\displaystyle{\displaystyle\otimes:\mathbf{C}\times\mathbf{C}\rightarrow\mathbf{C}}}$. Since Mag, the category of magmas, has cartesian products, we can therefore consider magma objects in the category Mag. These are called auto magma objects. There is a more direct definition: an auto magma object is a set ${\displaystyle{\displaystyle X}}$ together with a pair of binary operations ${\displaystyle{\displaystyle f,g:X\times X\rightarrow X}}$ satisfying ${\displaystyle{\displaystyle g(f(x,y),f(x^{\prime},y^{\prime}))=f(g(x,x^{\prime}),g(y,y^{\prime}))}}$ for all ${\displaystyle{\displaystyle x,x^{\prime},y,y^{\prime}}}$ in ${\displaystyle{\displaystyle X}}$. A medial magma is the special case where these operations are equal.

مزود بجداء ديكارتي. ويعتبر شكلا داخليا لتعريف العملية الثنائية ضمن التصنيف .