Related papers: A general context for Goodwillie Calculus
Abstract clones serve as an algebraic presentation of the syntax of a simple type theory. From the perspective of universal algebra, they define algebraic theories like those of groups, monoids and rings. This link allows one to study the…
We construct the unitary analogue of orthogonal calculus developed by Weiss, utilising model categories to give a clear description of the intricacies in the equivariance and homotopy theory involved. The subtle differences between real and…
We introduce the notion of an approximation system as a generalization of Taylor approximation, and we give some first examples. Next we develop the general theory, including error bounds and a sufficient criterion for convergence. More…
Multivector fields and differential forms at the continuum level have respectively two commutative associative products, a third composition product between them and various operators like $\partial$, $d$ and $*$ which are used to describe…
We define a simplicial differential calculus by generalizing divided differences from the case of curves to the case of general maps, defined on general topological vector spaces, or even on modules over a topological ring K. This calculus…
Quantiles, expectiles and extremiles can be seen as concepts defined via an optimization problem, where this optimization problem is driven by two important ingredients: the loss function as well as a distributional weight function. This…
Expectiles are statistical parameters which also provide a class of sublinear risk measures in finance. They are solutions of continuous optimization problems. The corresponding first order condition provides two different fixed point…
A stable $\infty$-category is $1$-semiadditive if the norms for all finite group actions are equivalences. In the presence of $1$-semiadditivity, Goodwillie calculus simplifies drastically. We introduce two variants of $1$-semiadditivity…
The purpose of this survey is to present in a uniform way the notion of equivalence between strict $n$-categories or $(\infty,n)$-categories, and inside a strict $(n+1)$-category or $(\infty,n+1)$-category.
We show that one can use model categories to construct rational orthogonal calculus. That is, given a continuous functor from vector spaces to based spaces one can construct a tower of approximations to this functor depending only on the…
We generalize the small object argument in order to allow for its application to proper classes of maps (as opposed to sets of maps in Quillen's small object argument). The necessity of such a generalization arose with appearance of several…
We show Goodwillie's calculus of functors and $n$-geometric $D^{-}$-stacks share similar features by starting to focus on the convergence of Taylor towers for homotopy functors and the fact that $\mathbb{R} F(A) \cong \text{holim}…
Under a general structural equation framework for causal inference, we provide a definition of the causal effect of a variable X on another variable Y, and propose an approach to estimate this causal effect via the use of instrumental…
We provide a geometric condition that guarantees strong Wilf equivalence in the generalized factor order. This provides a powerful tool for proving specific and general Wilf equivalence results, and several such examples are given.
In this paper the concept of compatible weak factorization systems in general categories is introduced as a counterpart of compatible complete cotorsion pairs in abelian categories. We describe a method to construct model structures on…
We show that differential calculus (in its usual form, or in the general form of topological differential calculus) can be fully imdedded into a functor category (functors from a small category of anchord tangent algebras to anchored sets).…
We study nilpotency in the context of exact Mal'tsev categories taking central extensions as the primitive notion. This yields a nilpotency tower which is analysed from the perspective of Goodwillie's functor calculus. We show in particular…
We restate the notion of orthogonal calculus in terms of model categories. This provides a cleaner set of results and makes the role of O(n)-equivariance clearer. Thus we develop model structures for the category of n-polynomial and…
In this article, we use a class of harmonic functions (maybe multi-valued) to study the equality part in a weighted version of Suita conjecture for higher derivatives and finite points case, and we obtain some sufficient and necessary…
An introduction to the physics and mathematics of the expanding universe, using no more than high-school level / undergraduate mathematics. Covered are the basics of scale factor expansion, the dynamics of the expanding universe, various…