Directional derivatives and higher order chain rules for abelian functor calculus
نویسندگان
چکیده
منابع مشابه
Wintenberger’s Functor for Abelian Extensions
Let k be a finite field. Wintenberger used the field of norms to give an equivalence between a category whose objects are totally ramified abelian p-adic Lie extensions E/F , where F is a local field with residue field k, and a category whose objects are pairs (K,A), where K ∼= k((T )) and A is an abelian p-adic Lie subgroup of Autk(K). In this paper we extend this equivalence to allow Gal(E/F ...
متن کاملFunctor Calculus and Operads
Speaker: Gregory Arone (Virginia) Title: Part 1: operads, modules and the chain rule Abstract: Let F be a homotopy functor between the categories of pointed topological spaces or spectra. By the work of Goodwillie, the derivatives of F form a symmetric sequence of spectra ∂∗F . This symmetric sequence determines the homogeneous layers in the Taylor tower of F , but not the extensions in the tow...
متن کاملA Higher-Order Calculus for Categories
A calculus for a fragment of category theory is presented. The types in the language denote categories and the expressions functors. The judgements of the calculus systematise categorical arguments such as: an expression is functorial in its free variables; two expressions are naturally isomorphic in their free variables. There are special binders for limits and more general ends. The rules for...
متن کاملA Reflective Higher-order Calculus
The π-calculus is not a closed theory, but rather a theory dependent upon some theory of names. Taking an operational view, one may think of the π-calculus as a procedure that when handed a theory of names provides a theory of processes that communicate over those names. This openness of the theory has been exploited in π-calculus implementations, where ancillary mechanisms provide a means of i...
متن کاملThe Chain Rule for Higher Derivatives
Perhaps the most important theorem of elementary differential calculus is the Chain Rule. It states, roughly, that the composite of two differentiable functions is again differentiable, and it gives a formula for the derivative of this composite. A Chain Rule of Order n should state, roughly, that the composite of two functions that are n times differentiable is again n times differentiable, an...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2018
ISSN: 0166-8641
DOI: 10.1016/j.topol.2017.12.010