In category theory, a branch of mathematics, a natural transformation provides a way of transforming one functor into another while respecting the internal structure (i.e., the composition of morphisms) of the categories involved. Hence, a natural transformation can be considered to be a "morphism of functors". Informally, the notion of a natural transformation states that a particular map between functors can be done consistently over an entire category. Indeed, this intuition can be formalized to define so-called functor categories. Natural transformations are, after categories and functors, one of the most fundamental notions of category theory and consequently appear in the majority of its applications. (Wikipedia).
Geogebra Video: Transformation Functions
Create a function and the make it with animation with geogebra. like the video will be explain transformation about a function
From playlist Geogebra Videos
Category Theory 1.6 : Natural Transformations
In this video, I will introduce natural transformations between (covariant) functors, and the category of functors. Translate This Video : http://www.youtube.com/timedtext_video?v=YIAaZxGOyl0&ref=share Notes : None yet Patreon : https://www.patreon.com/user?u=16481182 Teespring : https://
From playlist Category Theory
👉 Learn about dilations. Dilation is the transformation of a shape by a scale factor to produce an image that is similar to the original shape but is different in size from the original shape. A dilation that creates a larger image is called an enlargement or a stretch while a dilation tha
From playlist Transformations
In this video, I define a cool operation called the symmetrization, which turns any matrix into a symmetric matrix. Along the way, I also explain how to show that an (abstract) linear transformation is one-to-one and onto. Finally, I show how to decompose and matrix in a nice way, sort of
From playlist Linear Transformations
👉 Learn about dilations. Dilation is the transformation of a shape by a scale factor to produce an image that is similar to the original shape but is different in size from the original shape. A dilation that creates a larger image is called an enlargement or a stretch while a dilation tha
From playlist Transformations
From playlist Functions as transformations
Showing something is a linear transformation Check out my Linear Equations playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmD_u31hoZ1D335sSKMvVQ90 Subscribe to my channel: https://www.youtube.com/channel/UCoOjTxz-u5zU0W38zMkQIFw
From playlist Linear Transformations
Linear Transformations and Linear Systems
In this video we discuss linear transformations. We start by examining the mathematical definition of a linear transformation and apply it to several examples including matrix multiplication and differentiation. We then see how linear transformations relate to linear systems (AKA linear
From playlist Linear Algebra
Categories 3 Natural transformations
This lecture is part of an online course on category theory. We define natural isomorphisms and natural transformations of functors, and give some examples. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj51F9XZ_Ka4bLnQoxTdMx0AL
From playlist Categories for the idle mathematician
Morphisms of Fibered Categories
The two category structure of fibered categories. We will need this for morphisms of Gerbes in the future.
From playlist Stacks
Category Theory 1.7: Horizontal Composition and 2-Categories
In this video, I introduce the horizontal composition of natural transformations, the interchange rule, and the basics of 2-Categories/Bicategories. Translate This Video : Notes : None yet Patreon : https://www.patreon.com/user?u=16481182 Teespring : https://teespring.com/stores/fematika
From playlist Category Theory
Uniform p-adic wave front sets and zero loci of function ...- R.Cluckers - Workshop 2 - CEB T1 2018
Raf Cluckers (CNRS – Université de Lille & KU Leuven) / 08.03.2018 Uniform p-adic wave front sets and zero loci of functions of C exp-class. I will recall some concrete parts of the course on motivic integration given at the IHP by Halupczok, and use it to define distributions of Cexp cl
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Diff EQ Battle 4: Nonconstant Coefficients!
TABLE of Laplace transforms: https://web.stanford.edu/~boyd/ee102/laplace-table.pdf First-order linear differential equations explanation: https://youtu.be/F41dOHrrM9I Laplace transform of tf(t): https://youtu.be/8FxMAeiDgws Laplace transform of y'': https://youtu.be/xwEqM91S-mA Laplace
From playlist Differential Equation Battles
Fourier Transforms: Image Compression, Part 1
Data Science for Biologists Fourier Transforms: Image Compression Part 1 Course Website: data4bio.com Instructors: Nathan Kutz: faculty.washington.edu/kutz Bing Brunton: faculty.washington.edu/bbrunton Steve Brunton: faculty.washington.edu/sbrunton
From playlist Fourier
Reconsidering natural numbers and arithmetical expressions | Data structures Math Foundations 185
It is time to turn our gaze back to the true foundations of the subject: arithmetic with natural numbers. But now we know that the issue of "What exactly is a natural number?" is fraught with subtlety. We adopt a famous dictum of Errett Bishop, and start to make meaningful distinctions bet
From playlist Math Foundations