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Based on the algebraico-categorical (:sheaf-theoretic and sheafcohomological) conceptual and technical machinery of Abstract DifferentialGeometry, a new, genuinely background spacetime manifold independent, fieldquantization scenario for vacuum Einstein gravity and free Yang-Mills theoriesis introduced. The scheme is coined `third quantization' and, although itformally appears to follow a canonical route, it is fully covariant, because itis an expressly functorial `procedure'. Various current and future QuantumGravity research issues are discussed under the light of 3rd-quantization. Apostscript gives a brief account of this author's personal encounters withRafael Sorkin and his work.Comment: 43 pages; latest version contributed to a fest-volume celebrating  Rafael Sorkin's 60th birthday (Erratum: in earlier versions I had wrongly  written that the Editor for this volume is Daniele Oriti, with CUP as  publisher. I apologize for the mistake.

‘Third’ Quantization of Vacuum Einstein Gravity and Free Yang–Mills Theories