Definition:Right Cancellable Mapping
From ProofWiki
Definition
A mapping $f: X \to Y$ is right cancellable (or right-cancellable) if:
- $\forall Z: \forall h_1: Y \to Z, h_2: Y \to Z: h_1 \circ f = h_2 \circ f \implies h_1 = h_2$
Also known as right cancellative.
Also see
In the context of abstract algebra:
from which it can be seen that a right cancellable mapping can be considered as a right cancellable element of an algebraic structure whose operation is composition of mappings.
Sources
- George McCarty: Topology: An Introduction with Application to Topological Groups (1967): $\text{I}$: Problem $\text{BB}$
- T.S. Blyth: Set Theory and Abstract Algebra (1975): $\S 5$
- H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability (1996): Appendix $\text{A}.5$
