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Fields as algebraic objects. For vector and tensor fields, use eg. [dg.differential-geometry]. For physical fields, use eg. [mp.mathematical-physics] or [quantum-field-theory].

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In what sense are fields an algebraic theory?

Using the classification language given in Adamek/Herrlich/Strecker ("Abstract and Concrete Categories", Dover, 2009), every essentially algebraic category is necessarily complete, cocomplete, and wel …
Stephen Rodabaugh's user avatar