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  "body": "\n## Definition\n\nA *magma* is a pair $(M, \\cdot)$, where $M$ is a [[set|0SJ3RX9TXA]] and $\\cdot \\colon M \\times M \\to M$ is a [[binary operation|0M418FE7BB]] on $M$.\nA *homomorphism* of magmas $(M, \\cdot)$ and $(N, *)$ is a map $h \\colon M \\to N$ with $h(x \\cdot y) = h(x) * h(y)$ for all $x, y \\in M$.\n\n## Remarks\n\nExample: $(\\Z, -)$ is a magma, since the difference of two integers is an integer.\nIt is not associative: $(1 - 1) - 1 = -1$ but $1 - (1 - 1) = 1$.\n\nNon-example: $(\\N, -)$ is not a magma, since $1 - 2 \\notin \\N$, so subtraction is not a binary operation on $\\N$.\n\nThe empty set with the empty operation is a magma.\nThe word *groupoid* is an older name for a magma.\n",
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