quasi-separated morphism
scheme morphism 𝑓: 𝑋→𝑌 whose diagonal map 𝑋 → 𝑋 ×_𝑌 𝑋 is quasicompact
separated morphism
scheme morphism 𝑓: 𝑋→𝑌 whose diagonal map 𝑋 → 𝑋 ×_𝑌 𝑋 is a closed immersion
scheme morphism 𝑓: 𝑋→𝑌 whose diagonal map 𝑋 → 𝑋 ×_𝑌 𝑋 is quasicompact