Topos theory MOC

Subobject classifier

In a finitely complete category 𝖢, a subobject classifier is a morphism ⊤ :1 →Ω such that for any monomorphism (think subobject) 𝑠 :𝑆 ↣𝑋, there is a unique morphism 𝜒𝑠 such that

is a pullback square. #m/def/topos In other words, every subobject is the pullback of tt along a unique characteristic morphism. We think of Ω as an object of truth values, and the generalized element ⊤ as true.¹

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