nLab linear subspace

Idea

A linear subspace of an $R$-module $A$ is a concrete subobject of $A$ in the category ${}_R Mod$.

The stuff of a linear subspace of $A$ is a subset of $|A|$; it has the property of being closed under the module operations $0$, $+$ and $r \cdot$ inherent in $A$.

Related concepts

• linear map

• subobject, subspace

• Hilbert lattice, quantum logic