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 the calculus of functors, often also named Goodwillie calculus. While studying at Harvard University, Goodwillie...

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

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...

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...

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

(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...

(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...

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...

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

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

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

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

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

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...

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

dimension, as in knot theory. It is studied categorically via the "calculus of functors" by Thomas Goodwillie Archived 2009-11-28 at the Wayback Machine...

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

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

Cat of all small categories (with functors as morphisms) is Cartesian closed; the exponential CD is given by the functor category consisting of all functors...

logic, also called predicate logic, predicate calculus, or quantificational logic, is a collection of formal systems used in mathematics, philosophy...

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

doi:10.1007/BF01220869. S2CID 124051153. Świrszcz, Tadeusz (1974). "Monadic functors and convexity". Bulletin l'Académie Polonaise des Science, Série des Sciences...

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

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...

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...

Michael Winter have illustrated the method of lifting traditional logical expressions of topology to calculus of relations in their book Relational Topology...

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

Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that...