Meaning of symbol $\looparrowright$ in math

Question

Is there a conventional meaning for the symbol $\looparrowright$ when used in math.

I came across this symbol in here (see slide 2 for e.g.).

Answer 1

I personally sometimes use it as another way for epimorphism/surjection when additional distinction matters: just like $\hookrightarrow$ is reserved for an inclusion map as many people do while $\rightarrowtail$ is for general injection, I reserve $\looparrowright$ for a map from $X$ to its decomposition (dual of inclusion map), while $\twoheadrightarrow$ is for general surjection.