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u ever think about how a sub-object of X is the same thing as a truth value-valued functions on X?

any hot take on what a quotient object is?

idk but i'll pog when i see it

in nice cases a quotient object of X is an internal equivalence relation on X, or to be really fancy, an internal 0-groupoid on X

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and

this is notably true in much greater generality than for categories with a subobject classifier, e.g. for groups, rings, modules