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.
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
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