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  "body": "\n## Definition\n\nLet $\\mathcal{V}$ be a [[variety of algebras|AJNZJD8442]] and let $n \\ge 2$.\nA *Taylor term* for $\\mathcal{V}$ is an $n$-ary [[term|N9M2N27END]] $t(x_1, \\dots, x_n)$ such that:\n\n1. $t$ is [[idempotent|9FS1JFZSX4]], that is, $\\mathcal{V}$ satisfies $t(x, x, \\dots, x) \\approx x$.\n2. For each $i \\in \\set{1, \\dots, n}$, $\\mathcal{V}$ satisfies an [[identity|PKD440G2XW]] $t(u_1, \\dots, u_n) \\approx t(v_1, \\dots, v_n)$ with $u_i = x$ and $v_i = y$.\n   Here every $u_j$ and every $v_j$ is one of the two variables $x$ and $y$.\n\nAn algebra has a Taylor term if the variety it generates has one.\n\n## Remarks\n\nExample: a semilattice term $x \\wedge y$ is a Taylor term of the variety of semilattices.\nCheck: $x \\wedge x \\approx x$, and the identity $x \\wedge y \\approx y \\wedge x$ has $x$ on the left and $y$ on the right in place $1$.\nSwapping the names of $x$ and $y$ in it gives the required identity for place $2$.\nNon-example: in the variety of sets with no operations, the term $x_1$ is idempotent but fails clause 2 for $i = 1$.\nAn identity with $x_1$ on both sides reads $u_1 \\approx v_1$, which is false for $u_1 = x$ and $v_1 = y$.\nEvery [[majority term|9879ZMW5AA]] and every [[Mal'cev term|Y203PPTS61]] is a Taylor term.\nFor a majority term $m$, the identity $m(x, x, y) \\approx m(y, x, x)$ serves places $1$ and $3$, and $m(x, y, x) \\approx m(x, x, y)$ handles place $2$ after renaming.\n",
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