Morphism of locally ringed spaces
= Morphism of locally ringed spaces
{title2=$f_x^\#: \mathcal O_{Y,f(x)}\to\mathcal O_{X,x}$}
A morphism is a continuous map $f:X\to Y$ together with a homomorphism $\mathcal O_Y\to f_*\mathcal O_X$ of <sheaves of rings> whose induced map on every <stalk> is a <local homomorphism>. Applied to <schemes>, this is exactly a <morphism of schemes>.