relationship are known as adjoint functors, one being the left adjoint and the other the right adjoint. Pairs of adjoint functors are ubiquitous in mathematics...
63 KB (9,959 words) - 17:47, 25 September 2024
Look up adjoint in Wiktionary, the free dictionary. In mathematics, the term adjoint applies in several situations. Several of these share a similar formalism:...
1 KB (194 words) - 09:14, 18 September 2023
pairs of adjoint functors. Functors sometimes appear in functional programming. For instance, the programming language Haskell has a class Functor where...
24 KB (3,513 words) - 02:56, 11 August 2024
Limit (category theory) (redirect from Continuous functor)
colimits, like the strongly related notions of universal properties and adjoint functors, exist at a high level of abstraction. In order to understand them...
28 KB (4,352 words) - 03:41, 22 March 2024
concept of adjoint functors was introduced independently by Daniel Kan in 1958. Mathematics portal Free object Natural transformation Adjoint functor Monad...
24 KB (3,936 words) - 02:15, 26 February 2024
to the defining properties of pairs of adjoint functors in category theory, and this is where adjoint functors got their name from. Mathematical concepts...
18 KB (3,265 words) - 23:54, 11 January 2024
Monad (category theory) (redirect from Monadic functor)
are functors adjoint to each other, then T = G ∘ F {\displaystyle T=G\circ F} together with η , μ {\displaystyle \eta ,\mu } determined by the adjoint relation...
30 KB (4,467 words) - 15:23, 8 August 2024
properties and adjoint functors. Let 1 be the discrete category with a single object (denoted by •), and let U : C → 1 be the unique (constant) functor to 1. Then...
11 KB (1,336 words) - 16:25, 21 January 2024
Topos (redirect from Logical functors)
: X → Y {\displaystyle u:X\to Y} is a pair of adjoint functors (u∗,u∗) (where u∗ : Y → X is left adjoint to u∗ : X → Y) such that u∗ preserves finite limits...
33 KB (4,371 words) - 10:40, 21 September 2024
mathematics, the formal criteria for adjoint functors are criteria for the existence of a left or right adjoint of a given functor. One criterion is the following...
6 KB (752 words) - 16:31, 16 August 2024