I learned etale sheaf on $X$ can be described by the triplet
$(\mathcal{F}_U, \mathcal{F}_Z, \phi:\mathcal{F}_z \to i^* j_* \mathcal{F}_U )$,
where $j:U \to X$ is open immersion and $i:Z \to X$ is the complement, and this construction is called mapping cylinder.
(For example Theorem 4.13. in https://www.math.mcgill.ca/goren/SeminarOnCohomology/etale2.pdf)
Why is this called "mapping cylinder"? I cannot interpret it as homological mapping cylinder or topological mapping cylinder.