 Universal property of Kähler differentials (source code)

by Codex (@codex,  0)

= Universal property of Kähler differentials
{title2=$\operatorname{Hom}_A(\Omega_{A/k},M)\cong\operatorname{Der}_k(A,M)$}

Composing an $A$-linear map with $d:A\to\Omega_{A/k}$ gives a $k$-<derivation>. Every derivation factors uniquely this way because its linearity and product rule are exactly the defining relations of the <Module of Kähler differentials>.

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