Skip to main content
Post Made Community Wiki by Harry Gindi
LaTeXiFiEd
Source Link
Harry Gindi
  • 19.6k
  • 16
  • 123
  • 215

The yoneda lemma gives us a characterization of Psh(C)$Psh(\mathcal{C})$ that seems very similar to the theory of distributions. That is, we have a notion of representable presheaves, similar to representable distributions. The ability to talk about presheaves as colimits of representables correlates to the more complicated notion of distributions as derivatives and limits of representables. The whole idea of "test objects" is exactly the same as the notion of "test functions" and so on. Is there a deep connection there or is it just another case of stretching the terminology?

The yoneda lemma gives us a characterization of Psh(C) that seems very similar to the theory of distributions. That is, we have a notion of representable presheaves, similar to representable distributions. The ability to talk about presheaves as colimits of representables correlates to the more complicated notion of distributions as derivatives and limits of representables. The whole idea of "test objects" is exactly the same as the notion of "test functions" and so on. Is there a deep connection there or is it just another case of stretching the terminology?

The yoneda lemma gives us a characterization of $Psh(\mathcal{C})$ that seems very similar to the theory of distributions. That is, we have a notion of representable presheaves, similar to representable distributions. The ability to talk about presheaves as colimits of representables correlates to the more complicated notion of distributions as derivatives and limits of representables. The whole idea of "test objects" is exactly the same as the notion of "test functions" and so on. Is there a deep connection there or is it just another case of stretching the terminology?

Source Link
Harry Gindi
  • 19.6k
  • 16
  • 123
  • 215

Distributions as presheaves?

The yoneda lemma gives us a characterization of Psh(C) that seems very similar to the theory of distributions. That is, we have a notion of representable presheaves, similar to representable distributions. The ability to talk about presheaves as colimits of representables correlates to the more complicated notion of distributions as derivatives and limits of representables. The whole idea of "test objects" is exactly the same as the notion of "test functions" and so on. Is there a deep connection there or is it just another case of stretching the terminology?