Physical fields are identified with functors between groupoids, with classical fields as the special case where the probing groupoid is a set.
Higher Topos Theory in Physics
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A brief exposition of the point of higher topos theory in (mathematical) physics, commissioned for the Encyclopedia of Mathematical Physics 2nd ed.
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"Fields" in classical and quantum field theories
Physical fields are identified with functors between groupoids, with classical fields as the special case where the probing groupoid is a set.