Difference between revisions of "Composition"
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Compsition can be thought of as a data type in [[Category Theory]]<ref>{{:Video/Intro to Category Theory I: the Data of a Category}}</ref>. It is often made of [[object]]s and [[map]]s. Composition is closely related to [[Monad]] and [[Symmetry]]. | Compsition can be thought of as a data type in [[Category Theory]]<ref>{{:Video/Intro to Category Theory I: the Data of a Category}}</ref>. It is often made of [[object]]s and [[map]]s. In [[Category Theory]], compositions must obey the rule of [[associativity]], which preserves sequential invariance at the [[map]] level. Composition is closely related to [[Monad]] and [[Symmetry]]. | ||
{{:Meta-Rule/Composition}} | {{:Meta-Rule/Composition}} | ||
Revision as of 02:54, 27 March 2022
Compsition can be thought of as a data type in Category Theory[1]. It is often made of objects and maps. In Category Theory, compositions must obey the rule of associativity, which preserves sequential invariance at the map level. Composition is closely related to Monad and Symmetry.
Symmetries as the first Meta-Rule
According to Mathemaniac, symmetries can be thought of as mathematical operands that gets to be manipulated through some operations that preserves the properties of being symmetrical. These four most general properties are:
- Closure: Symmetrical operations on symmetries always create symmetries
- Associativity: Symmetries composition with symmetries are symmetries Associative
- Identity/Unit: Doing nothing is a symmetrical operation
- Inverse Exists: Symmetrical operations can be undone, and returns to the original symmetry.
A mathematical treatment of this subject was explained by Norm Wilberger in a video[2].
Talks about Combinators and Enumerable Sets here
Particularly talks about SK Combinators, and showing that these ideas, and enumerability, determines whether certain kinds of building blocks can be recursively composed or not. Watch Dana Scott's lecture 3[3]on Lambda Calculus.
References
Related Pages
- ↑ Mann, Jeremy (Jun 25, 2020). Intro to Category Theory I: the Data of a Category. local page: Jeremy Mann.
- ↑ Wildberger, Norman J. (Nov 24, 2021). A (somewhat) new paradigm for mathematics and physics. local page: Insights into Mathematics.
- ↑ Recursively Enumerable Sets