functors which are sufficiently good approximations for certain purposes. The calculus of functors was developed by Thomas Goodwillie in a series of three...

especially famous for developing the concept of calculus of functors, often also named Goodwillie calculus. While studying at Harvard University, Goodwillie...

homology of spaces of long knots in codimension >2", with P. Lambrechts and V. Turchin, Geometry & Topology, 14 (2010), 2151–2187. "Calculus of functors, operad...

functors: for instance, a differentiable manifold is also a topological manifold, and a differentiable map is also continuous, so there is a functor Diff...

(i.e. sets of morphisms between objects) give rise to important functors to the category of sets. These functors are called hom-functors and have numerous...

isomorphisms). It allows the embedding of any locally small category into a category of functors (contravariant set-valued functors) defined on that category. It...

are polynomial functors from V {\displaystyle {\mathcal {V}}} to V {\displaystyle {\mathcal {V}}} ; these two are also Schur functors. The notion appears...

called sentence-functors, and logical connectives are also called truth-functors. An argument is defined as a pair of things, namely a set of sentences, called...

via the "calculus of functors" by Thomas Goodwillie, John Klein, and Michael S. Weiss. A mathematical rose with k petals is an immersion of the circle...

localization See Bousfield localization. calculus of functors The calculus of functors is a technique of studying functors in the manner similar to the way a...

typed lambda calculus ( λ → {\displaystyle \lambda ^{\to }} ), a form of type theory, is a typed interpretation of the lambda calculus with only one...

rational calculations. Goodwillie, motivated by his "calculus of functors", conjectured the existence of a theory intermediate to K-theory and Hochschild...

developed Embedding Calculus, a Calculus of functors for embeddings of manifolds. In 2006, he was awarded the Fröhlich Prize of the London Mathematical Society...

First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy, linguistics...

Willard Quine, 1976, "Algebraic Logic and Predicate Functors" pages 283 to 307 in The Ways of Paradox, Harvard University Press. Historical perspective...

representing objects of the functors D i f f k {\displaystyle \mathrm {Diff} _{k}} and related functors. Seen from this point of view calculus may in fact be...

isomorphism (or sometimes natural equivalence or isomorphism of functors). Two functors F {\displaystyle F} and G {\displaystyle G} are called naturally...

(1972) survey the early history of combinatory logic. For a more modern treatment of combinatory logic and the lambda calculus together, see the book by Barendregt...

contravariant functor acts as a covariant functor from the opposite category Cop to D. A natural transformation is a relation between two functors. Functors often...

adjunction of any functor with its inverse. Category theory views these collection monads as adjunctions between the free functor and different functors from...

examples of mappings that are invertible up to homotopy; and so large classes of homotopy equivalent spaces[clarification needed]. Calculus of fractions...

Saunders; Moerdijk, Ieke (1992). "Chapter I. Categories of Functors; sections 7. Propositional Calculus, 8. Heyting Algebras, and 9. Quantifiers as Adjoints"...

grammar shares some features with the simply typed lambda calculus. Whereas the lambda calculus has only one function type A → B {\displaystyle A\rightarrow...

confused with other uses of the word "functor" throughout mathematics, see Functor (disambiguation). In the untyped lambda calculus, all functions are higher-order;...

semantic values can be interpreted, transferred also for functors (except for intensional functors, they have only intension). As mentioned, motivations...

same as a contravariant functor from O ( X ) {\displaystyle O(X)} to C {\displaystyle C} . Morphisms in this category of functors, also known as natural...

from lambda calculus, such as LISP and Scheme, and also in functional languages. It has a role in the study of the denotational semantics of computer programs...

number of algebraic devices called predicate functors (or predicate modifiers) that operate on terms to yield terms. PFL is mostly the invention of the logician...

Group representations are functors from groups, seen as one-object categories, into FinVect. DisCoCat models are monoidal functors from a pregroup grammar...

let F: A → B be a functor of abelian categories. There are two dual concepts: right derived functors come from left exact functors and are calculated...