I added a new easy to prove proposition to my book:

**Proposition** An endofuncoid $latex f$ is $latex T_{1}$-separable iff $latex \mathrm{Cor}\langle f\rangle^{\ast}\{x\}\sqsubseteq\{x\}$ for every $latex x\in\mathrm{Ob}\, f$.

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I added a new easy to prove proposition to my book:

**Proposition** An endofuncoid $latex f$ is $latex T_{1}$-separable iff $latex \mathrm{Cor}\langle f\rangle^{\ast}\{x\}\sqsubseteq\{x\}$ for every $latex x\in\mathrm{Ob}\, f$.