Definition:Left Cancellable Mapping
From ProofWiki
Definition
A mapping $f: Y \to Z$ is left cancellable (or left-cancellable) if:
- $\forall X: \forall g_1: X \to Y, g_2: X \to Y: f \circ g_1 = f \circ g_2 \implies g_1 = g_2$
Also known as left cancellative.
Also see
In the context of abstract algebra:
from which it can be seen that a left cancellable mapping can be considered as a left 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 $\text{A}.5$
