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Questions of the kind "What's the name for a X that satisfies property Y?"

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What name can I use for a cocone over the mapping cone diagram?

In homotopy theory, the mapping cone of a continuous map $f\colon X \to Y$ is the homotopy pushout over the following span: $$ \require{AMScd} \begin{CD} X @>{f}>> Y\\ @VVV \\ \{*\} \end{CD} $$ I.e. …
John Gowers's user avatar