Symbols:T

Set

 * $T$

Used to denote a general set, often in conjunction with $S$ when more than one set is under discussion.

Algebraic Substructure

 * $T$

Used to denote a general algebraic substructure, of the algebraic structure $S$, in particular a subsemigroup.

In this context, frequently seen in the compound symbol $\left({T, \circ}\right)$ where $\circ$ represents an arbitrary binary operation.

General binary operation

 * $\intercal$

Used in to denote an arbitrary binary operation in a general algebraic structure.

It is given the name truc, pronounced trook, French for trick or technique.

himself suggests that truc could be translated as thingummyjig, but this is linguistically unsupported.