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An explicit description of Lawvere's segment in the category of simplicial sets

I've never heard this called 'Lawvere's segment' before, but your $L$ is the subobject classifier in the presheaf topos $[A^{\mathrm{op}},\mathrm{Set}]$. In presheaf toposes generally, the subobject …
Finn Lawler's user avatar
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