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\bigsqcup does work: 
\bigsqcap does not work Failed to parse (unknown function "\bigsqcap"): {\displaystyle \quad\bigsqcap\quad}
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Using ∏ is oK outside of mathematical context, but does not work within math-environment: Failed to parse (syntax error): {\displaystyle ∏}
⊓ ∏ ⊔ ∐ 
