Complex of Abelian groups

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I will be grateful if someone could explain the meaning of product notation in the following paragraphs:

  • From pp. 35 of Liu's Algebraic Geometry and Arithmetic Curves: (c) 2002, Qing Liu
  • Ravi Vakil's Foundations of Algebraic Geometry: (c) November 2017, Ravi Vakil

This is my first time ever reading about sheaves, and I don't have much exposure to category theory.