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by giraj
1748 days ago
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You're right, there's a missing step. By "a monoid M in the category C" we mean that M is an object in C along with two morphisms "unit" : 1 -> M and "multiplication" : M x M -> M satisfying the "monoid laws" translated to C. (And really C should be a so-called "monoidal category".) When C = Set, this gives the usual notion of a monoid, which classically is a set by definition, as you say. However there are lots of interesting monoid objects in other categories! |
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