# Demonic composition

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In mathematics, **demonic composition** is an operation on binary relations that is somewhat comparable to ordinary composition of relations but is robust to refinement of the relations into (partial) functions or injective relations.

Unlike ordinary composition of relations, demonic composition is not associative.

## Definition

Suppose *R* is a binary relation between *X* and *Y* and *S* is a relation between *Y* and *Z*. Their **right demonic composition** *R* **;**^{→} *S* is a relation between *X* and *Z*. Its graph is defined as

Conversely, their **left demonic composition** *R* **;**^{←} *S* is defined by

## References

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