In mathematics, the **category of magmas**, denoted **Mag**, is the category whose objects are magmas (that is, sets equipped with a binary operation), and whose morphisms are magma homomorphisms.

The category **Mag** has direct products, so the concept of a magma object (internal binary operation)^{[clarification needed]} makes sense. (As in any category with direct products.)

There is an inclusion functor: **Set → Med ↪ Mag** as trivial magmas, with operations given by projection: *x* T *y* = *y* .

An important property is that an injective endomorphism can be extended to an automorphism of a magma extension, just the colimit of the (constant sequence of the) endomorphism.

Because the singleton ({*}, *) is the zero object of **Mag**, and because **Mag** is algebraic, **Mag** is pointed and complete.^{[1]}

References

Borceux, Francis; Bourn, Dominique (2004). Mal'cev, protomodular, homological and semi-abelian categories. Springer. pp. 7, 19. ISBN 1-4020-1961-0.

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