1
$\begingroup$

Can you give a categorification of the Taylor polynomial of a real function $ f : U \subset \mathbb{R} \to \mathbb{R} $ defined by : $$ f(x) = f(a) + f'(a) (x-a) + \frac{1}{2} (x-a)^{2} + \dots + \dfrac{1}{n!} f^{(n)} (a) (x-a)^n + o (x^{n+1} ) $$ in a neighbourhood $ U $ of an element $ a \in \mathbb{R} $ ?

Thanks in advance for your help.

Improve this question
$\endgroup$
4
  • 2
    $\begingroup$ What does 'categorification' mean for you? This is an important idea in contemporary mathematics, but is not a defined technical term. If you mean it broadly, this seems okay (to me), but I think this should be made clear, so that it does not look like a defined question relative to some formal system. (I recognize that you already tagged it a 'soft-question'; I am not criticizing.) Also "limited development" seems a very unusual term to me; this is usually taught as the 'Taylor polynomial" around $a$. Also, "element of $a$" does not make sense. $\endgroup$
    – Peter Heinig
    Commented Sep 30, 2017 at 7:08
  • $\begingroup$ For me, categorification means a process which passes from a set to a category, or from a categorie to a $ 2 $ - category ... etc. $\endgroup$
    – YoYo
    Commented Sep 30, 2017 at 7:16
  • 6
    $\begingroup$ Look up "calculus of functors." It is a really spectacular categorification of Taylor series. $\endgroup$
    – Qiaochu Yuan
    Commented Sep 30, 2017 at 7:18
  • 4
    $\begingroup$ mathoverflow.net/questions/86464/surveys-of-goodwillie-calculus the references given here may also be helpful $\endgroup$
    – Harry Richman
    Commented Sep 30, 2017 at 8:12

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .