Funny identity matrix
Given any category C with finite products and coproducts such that the products distribute over the coproducts, you can make a compact closed bicategory Mat(C) of (natural numbers, matrices of elements of Ob(C), matrices of elements of Mor(C)) and define matrix composition by
Take the partial order whose objects are nonnegative integers and whose morphisms mean ; the product is gcd and the coproduct is lcm. In this category, the terminal object is 0 and the initial object is 1, so the identity matrix looks like
and matrix multiplication is
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