Orbital Overlap Diagram of CO (carbon monoxide)

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Both the carbon AND the oxygen are "sp" hybridized, and therefore the two hybrid orbitals are arranged LINEARLY.
THEN, one of the leftover 2p orbitals is drawn in the "up-down" direction ... they 'overlap' to make one of the pi bonds (the "double" bond).
The other leftover 2p orbital is drawn in the "forward-backward" direction, and they overlap to make the second pi bond (the "triple" bond).

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how is the pink pi bond an overlap between pz of C and pz of O if the pz of C is vacant? There must be a coordinate bond where the oxygen shares a lone pair of electrons with C to fill the pz vacant orbiatal. My question here is (Is the lone pair of electrons from O and given to the pz of C the one from the px of O hybridized in sp orbital?

karimhani