Protosandwiches are not sandwiches.
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Sandwiches are protosandwiches, there's a forgetful functor F such that F(s) ~= F(s') iff s ~= s'.
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Yes, all sandwiches are protosandwiches, but no protosandwich is a sandwich.
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Er, you're claiming S ⊆ P and S ∩ P = Ø, which literally implies no sandwich exists. Do you mean "proper protosandwiches"?
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What's your definition of a proper protosandwich?
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Let S be the category of sandwiches and P be the category of protosandwiches. We call an object p in P a proper protosandwich if there is no s in S such that F(s) = p, where F is the canonical embedding functor.
10:53 AM - 23 Nov 2017
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. Banned in Sweden. SubGenius, Zhuangist, white-hat troll. Defrocked mathematician. Brain problems.