- "Expression || Expression" -- see Expression -- the class of all expressions
- "Expression || Holder" -- see Expression -- the class of all expressions
- "Expression || Thing" -- see Expression -- the class of all expressions
- "Holder || Expression" -- see Expression -- the class of all expressions
- "Holder || Holder" -- see Expression -- the class of all expressions
- "Thing || Expression" -- see Expression -- the class of all expressions
- GradedModuleMap || GradedModuleMap -- a binary operator, often used for vertical concatenation
- Matrix || Matrix -- join matrices vertically
- "Matrix || Number" -- see Matrix || Matrix -- join matrices vertically
- "Matrix || RingElement" -- see Matrix || Matrix -- join matrices vertically
- "Number || Matrix" -- see Matrix || Matrix -- join matrices vertically
- "RingElement || Matrix" -- see Matrix || Matrix -- join matrices vertically
- "RingElement || RingElement" -- see Matrix || Matrix -- join matrices vertically
- Net || Net -- join nets or strings vertically
- Vector || Vector -- join Vectors

This operator may be used as a binary operator in an expression like x||y. The user may install binary methods for handling such expressions with code such as

X || Y := (x,y) -> ...

where X is the class of x and Y is the class of y.