# A category of matrices representing two categories of by Fomin A.A.

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By Fomin A.A.

Each τ -adic matrix represents either a quotient divisible team and a torsion-free, finite-rank team. those representations are an equivalence and a duality of different types, respectively.

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It just doesn’t matter. When we make shapes or patterns and measure them, we can choose any unit that we want to, keeping in mind that what we are really measuring is a proportion. I guess a simple example would be the perimeter of a square. ), then the perimeter would obviously be 4. What that really means is that for any square, the perimeter is four times as long as the side. This business of units is related to the idea of scale. If we take some shape and blow it up by a certain factor, say 2, then all of our length measurements on the big shape will come out just as if we were measuring the original shape with a half-size ruler.

There are no gaps between the tiles (I like to think of them as ceramic tiles, like in a mosaic), and the tiles don’t overlap. At least, that’s how it appears. Remember, the objects that we’re really talking about are perfect, imaginary shapes. Just because the picture looks good doesn’t mean 24 M E A S U R E M E N T that’s what is really going on. Pictures, no matter how carefully made, are part of physical reality; they can’t possibly tell us the truth about imaginary, mathematical objects. Shapes do what they do, not what we want them to do.

When we make shapes or patterns and measure them, we can choose any unit that we want to, keeping in mind that what we are really measuring is a proportion. I guess a simple example would be the perimeter of a square. ), then the perimeter would obviously be 4. What that really means is that for any square, the perimeter is four times as long as the side. This business of units is related to the idea of scale. If we take some shape and blow it up by a certain factor, say 2, then all of our length measurements on the big shape will come out just as if we were measuring the original shape with a half-size ruler.