Generalized left (right) inverse of a function

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Let $f:A\to B$ be a function.

I know that a function $g:B\to A$ such that $g\circ f=i_A$ is said to be a left inverse of the function $f$.

On the other hand a function $h:B\to A$ such that $f\circ h=i_B$ is said to be a right inverse of the function $f$.

Where $i_A$ and $i_B$ are the identity functions on the sets $A$ and $B$ respectively.

Recently I come across a term 'generalized left (right) inverse' and a claim that says :
A left inverse is also a generalized left inverse.

Can anyone please help me understand the term (definition would be sufficient).

I know there is a concept of 'generalized inverse' for matrix operations.
Is that concept somehow related here too?