Is light a type of matter and can it be affected by gravity?

In summary: Fermions take up space because they obey the Pauli exclusion principle. Bosons do not obey it, so they don't take up space, so they are not matter. However, you are correct that the majority of the mass of ordinary matter is due to the massive gauge bosons that mediate the strong interaction.
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I'm a sort of newcomer here, so this may have been answered elsewhere. But, as I understand, mass is tied to inertia. Isn't this why we're looking for Higgs? If so, are photons inertial? Then, the spacetime is Minkowskian. They themselves cannot create a non-Minkowskian spacetime that will affect nearby photons. If photons do have mass and can create a non_Minkowskian spacetime that can alter the parhs of nearby photons, then photons will interact. This gives rise to two further questions:
1. As I remember long-ago college, a fundamental result of QED is that photons cannot interact.
2. What mediates the interaction? If gravitons, then gravitons must be the quanta of still more elementary fields. Would this be correct?
 
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