Template:Cross-Relation Quotient Structure Inverse Completion Context Definition

This template is to be used to insert onto a page the specification of the scope of the quotient structure defined by the cross-relation in the context of the development of the theory of the inverse completion of a given commutative semigroup with cancellable elements.

The following is what is transcluded:

This cross-relation is a congruence relation on $S \times C$.

Let the quotient structure defined by $\boxtimes$ be:
 * $\left({T\,', \oplus\,'}\right) := \left({\dfrac {S \times C} \boxtimes, \oplus_\boxtimes}\right)$

where $\oplus_\boxtimes$ is the operation induced on $\dfrac {S \times C} \boxtimes$ by $\oplus$.