Template:Cross-Relation Quotient Structure Inverse Completion Context Definition

Template
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:
 * $\struct {T', \oplus'} := \struct {\dfrac {S \times C} \boxtimes, \oplus_\boxtimes}$

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