Can you give a categorification of the limited development 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 of $ a \in \mathbb{R} $ ?

Thanks in advance for your help.