diagonal morphism

Given $X\in {\mathsf{Sch}}_{/S}$, define the diagonal morphism as $\Delta_{X/S}: X\to X \underset{\scriptscriptstyle {S} }{\times} X$:

https://q.uiver.app/?q=WzAsNSxbMiw0LCJYIl0sWzQsNCwiUyJdLFs0LDIsIlgiXSxbMiwyLCJYXFxmaWJlcnByb2R7U30gWCJdLFswLDAsIlgiXSxbMiwxLCJmIl0sWzAsMSwiZiIsMl0sWzMsMCwiXFxwaV8xIiwyXSxbMywyLCJcXHBpXzIiXSxbNCwwLCJcXGlkX1giLDIseyJjdXJ2ZSI6NX1dLFs0LDIsIlxcaWRfWCIsMCx7ImN1cnZlIjotNX1dLFs0LDMsIlxcZXhpc3RzIFxcRGVsdGFfWCIsMCx7InN0eWxlIjp7ImJvZHkiOnsibmFtZSI6ImRhc2hlZCJ9fX1dXQ==