functors which are sufficiently good approximations for certain purposes. The calculus of functors was developed by Thomas Goodwillie in a series of three...
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Thomas Goodwillie (mathematician) (category Harvard University Department of Mathematics faculty)
especially famous for developing the concept of calculus of functors, often also named Goodwillie calculus. While studying at Harvard University, Goodwillie...
4 KB (321 words) - 06:16, 20 May 2024
Ismar Volić (category Year of birth missing (living people))
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...
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functors: for instance, a differentiable manifold is also a topological manifold, and a differentiable map is also continuous, so there is a functor Diff...
18 KB (2,310 words) - 22:06, 26 August 2024
(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...
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Yoneda lemma (redirect from Yoneda functor)
isomorphisms). It allows the embedding of any locally small category into a category of functors (contravariant set-valued functors) defined on that category. It...
20 KB (3,362 words) - 13:43, 2 August 2024
are polynomial functors from V {\displaystyle {\mathcal {V}}} to V {\displaystyle {\mathcal {V}}} ; these two are also Schur functors. The notion appears...
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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...
111 KB (11,054 words) - 07:19, 29 August 2024
Immersion (mathematics) (category Maps of manifolds)
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...
23 KB (2,861 words) - 01:58, 13 August 2024
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...
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typed lambda calculus ( λ → {\displaystyle \lambda ^{\to }} ), a form of type theory, is a typed interpretation of the lambda calculus with only one...
33 KB (4,587 words) - 10:39, 14 August 2024
rational calculations. Goodwillie, motivated by his "calculus of functors", conjectured the existence of a theory intermediate to K-theory and Hochschild...
76 KB (10,382 words) - 14:54, 23 June 2024
Michael Weiss (mathematician) (category Academic staff of the University of Münster)
developed Embedding Calculus, a Calculus of functors for embeddings of manifolds. In 2006, he was awarded the Fröhlich Prize of the London Mathematical Society...
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First-order logic (redirect from First-order predicate calculus)
First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy, linguistics...
93 KB (13,105 words) - 23:48, 26 August 2024
Algebraic logic (redirect from Calculus of relations)
Willard Quine, 1976, "Algebraic Logic and Predicate Functors" pages 283 to 307 in The Ways of Paradox, Harvard University Press. Historical perspective...
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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...
5 KB (730 words) - 15:46, 19 August 2023
Natural transformation (category Functors)
isomorphism (or sometimes natural equivalence or isomorphism of functors). Two functors F {\displaystyle F} and G {\displaystyle G} are called naturally...
33 KB (5,663 words) - 12:43, 25 June 2024
Combinatory logic (redirect from Combinator calculus)
(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...
41 KB (5,243 words) - 13:58, 25 August 2024
Category theory (redirect from Categorical point of view)
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...
34 KB (3,827 words) - 21:31, 20 August 2024
Monad (functional programming) (category CS1 maint: DOI inactive as of August 2024)
adjunction of any functor with its inverse. Category theory views these collection monads as adjunctions between the free functor and different functors from...
75 KB (9,300 words) - 08:42, 12 August 2024
examples of mappings that are invertible up to homotopy; and so large classes of homotopy equivalent spaces[clarification needed]. Calculus of fractions...
9 KB (1,346 words) - 22:44, 18 December 2022
Currying (category Lambda calculus)
Saunders; Moerdijk, Ieke (1992). "Chapter I. Categories of Functors; sections 7. Propositional Calculus, 8. Heyting Algebras, and 9. Quantifiers as Adjoints"...
36 KB (5,016 words) - 01:30, 27 August 2024
Categorial grammar (redirect from Lambek calculus)
grammar shares some features with the simply typed lambda calculus. Whereas the lambda calculus has only one function type A → B {\displaystyle A\rightarrow...
25 KB (3,689 words) - 05:32, 23 June 2024
confused with other uses of the word "functor" throughout mathematics, see Functor (disambiguation). In the untyped lambda calculus, all functions are higher-order;...
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semantic values can be interpreted, transferred also for functors (except for intensional functors, they have only intension). As mentioned, motivations...
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Sheaf (mathematics) (redirect from Global section functor)
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...
68 KB (10,956 words) - 07:22, 21 August 2024
Apply (category Adjoint functors)
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...
12 KB (1,449 words) - 01:00, 28 June 2023
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...
20 KB (3,078 words) - 07:15, 21 June 2024
FinVect (redirect from Category of finite dimensional K-vector spaces)
Group representations are functors from groups, seen as one-object categories, into FinVect. DisCoCat models are monoidal functors from a pregroup grammar...
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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...
29 KB (4,503 words) - 21:16, 26 April 2024