They are mixed everywhere and I can't find a single article that treats them right and with the required rigor they should get. Can someone explain them?

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    $\begingroup$ Try some of the work of Wu. He has thought a great deal about the best way to express many of the relations you are after. $\endgroup$ – lulu Sep 8 '16 at 19:26
  • $\begingroup$ Quotient can also mean partition by equivalence relation, in some sense quotient groups. $\endgroup$ – simonzack Sep 8 '16 at 19:27

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