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Applied category theory is an academic discipline in which methods from category theory are used to study other fields [1] [2] [3] including but not limited to ...
Categorical quantum mechanics is the study of quantum foundations and quantum information using paradigms from mathematics and computer science, notably monoidal category theory. The primitive objects of study are physical processes, and the different ways that these can be composed. It was pioneered in 2004 by Samson Abramsky and Bob Coecke.
For any commutative ring R, the category of R-algebras is monoidal with the tensor product of algebras as the product and R as the unit. The category of pointed spaces (restricted to compactly generated spaces for example) is monoidal with the smash product serving as the product and the pointed 0-sphere (a two-point discrete space) serving as ...
A spectrum in physics, such as the electromagnetic spectrum, is often termed as either continuous (with energy at all wavelengths) or discrete (energy at only certain wavelengths). In contrast, quantum mechanics uses quanta, certain defined amounts (i.e. categorical amounts) which are distinguished from continuous amounts.
an automorphism if f is both an endomorphism and an isomorphism. aut(a) denotes the class of automorphisms of a. a retraction if a right inverse of f exists, i.e. if there exists a morphism g : b → a with f ∘ g = 1 b. a section if a left inverse of f exists, i.e. if there exists a morphism g : b → a with g ∘ f = 1 a.
R, a language often used in data mining and statistical data analysis, is now also sometimes used for data wrangling. [6] Data wranglers typically have skills sets within: R or Python, SQL, PHP, Scala, and more languages typically used for analyzing data. Visual data wrangling systems were developed to make data wrangling accessible for non ...
This is a list of statistical procedures which can be used for the analysis of categorical data, also known as data on the nominal scale and as categorical variables. General tests [ edit ]
It does this by representing data as points in a low-dimensional Euclidean space. The procedure thus appears to be the counterpart of principal component analysis for categorical data. [citation needed] MCA can be viewed as an extension of simple correspondence analysis (CA) in that it is applicable to a large set of categorical variables.