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What's the semantic difference between \amalg and \coprod for disjoint unions?

I used to use \amalg for binary operations like X \amalg Y and \coprod for operators like \coprod_\lambda X_\lambda. But I realized that I don't know any literature or manual how these similar-looking symbols should be used. Please tell me if you have any.

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I found an answer by myself soon after I asked a question. To close this question, I write an answer by myself.

In a document in https://ctan.org/pkg/comprehensive, \amalg appears in "Table 50: Binary Operators" among \cup, \oplus and \setminus. On the other hand, \coprod appears in "Table 72: Variable-sized Math Operators" among \bigcup, \bigoplus and \sum. So these symbols should be used exactly as I described in the question.

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  • One can see from \coprod_0^n in both textstyle and displaystyle that it behaves in the manner of \sum. In contrast, \amalg does not change size/limit-style in displaystyle. As a binary operator, it behaves in the manner of + and -. – Steven B. Segletes May 2 '19 at 11:20
  • Thank you for pointing out the difference between their behavior. The real problem (led me to ask) is that I often annoyed when \coprod is used as a binary operator (but I don't have sound reasons for refusing). It would be better than my answer if there is some literature pointing out this as a common mistake. – Orat May 2 '19 at 11:34

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