Objects (category theory) | Topos theory
In category theory, a subobject classifier is a special object Ω of a category such that, intuitively, the subobjects of any object X in the category correspond to the morphisms from X to Ω. In typical examples, that morphism assigns "true" to the elements of the subobject and "false" to the other elements of X. Therefore, a subobject classifier is also known as a "truth value object" and the concept is widely used in the categorical description of logic. Note however that subobject classifiers are often much more complicated than the simple binary logic truth values {true, false}. (Wikipedia).
Lecture 5: The definition of a topos (Part 2)
A topos is a Cartesian closed category with all finite limits and a subobject classifier. In his two seminar talks (of which this is the second) James Clift will explain all of these terms in detail. In his first talk he defined products, pullbacks, general limits, and exponentials and in
From playlist Topos theory seminar
Topoi 2: The Subobject Classifier diagram
Topos, topoi, toposes. Previous video 1: https://youtu.be/Ysp7P4wW-zE This is the second video, discussing of the Subobject Classifier in a category of sets. For the followup video, just look at the videos uploaded one, two weeks later. The document used can be found here: https://gist.gi
From playlist Logic
Lecture 4: The definition of a topos (Part 1)
A topos is a Cartesian closed category with all finite limits and a subobject classifier. In his two seminar talks (of which this is the first) James Clift will explain all of these terms in detail. In this talk he defines products, pullbacks, general limits, and exponentials and in Part 2
From playlist Topos theory seminar
Intro to Subsequences | Real Analysis
What are subsequences in real analysis? In today's lesson we'll define subsequences, and see examples and nonexamples of subsequences. We can learn a lot about a sequence by studying its subsequence, so let's talk about it! If (a_n) is a sequence, we can denote a subsequence of (a_n) as (
From playlist Real Analysis
The Definition of a Surjective(Onto) Function and Explanation
The Definition of a Surjective(Onto) Function and Explanation
From playlist Functions, Sets, and Relations
Lecture 11: Sheaves form a topos (Part 2)
In this talk Patrick Elliott proves that the category of sheaves on a site is a topos, by discussing the exponentials and subobject classifier in detail. The notes are already online: The lecture notes are available here: http://therisingsea.org/notes/ch2018-lecture11.pdf. For the genera
From playlist Topos theory seminar
Lecture 13: Higher-order logic and topoi (Part 3)
In this talk James Clift explains how to think about quantifiers in the context of topoi using adjunctions, and more generally how to extract a type theory out of a topos. This provides the means to "cut out" subobjects using formulas, which is in turn the fundamental idea to defining clas
From playlist Topos theory seminar
Definition of a Surjective Function and a Function that is NOT Surjective
We define what it means for a function to be surjective and explain the intuition behind the definition. We then do an example where we show a function is not surjective. Surjective functions are also called onto functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear ht
From playlist Injective, Surjective, and Bijective Functions
Topoi 1: Predicates vs. subsets
Topos, topoi, toposes. This is the warmup video for the discussion of the Subobject Classifier in a category of sets, in the next video. The document used can be found here: https://gist.github.com/Nikolaj-K/469b9ca1c085ea4ac4e3d7d0008913f5 Typo: In minute 42, the membership relation on sh
From playlist Logic
AlgTopReview: An informal introduction to abstract algebra
This is a review lecture on some aspects of abstract algebra useful for algebraic topology. It provides some background on fields, rings and vector spaces for those of you who have not studied these objects before, and perhaps gives an overview for those of you who have. Our treatment is
From playlist Algebraic Topology
An introduction to subtraction, the terms and concepts involved, and subtraction as the opposite of addition. Some example problems are carefully worked and explained. From the Prealgebra course by Derek Owens. This course is available online at http://www.LucidEducation.com.
From playlist Prealgebra Chapter 1 (Complete chapter)
Eleftherios Pavlides & Thomas Banchoff - Hinge Elastegrities Shape Shifting - G4G12 April 2016
Named by analogy to tensegrity, maintaining form integrity through tension alone, hinge-elastegrity, maintaining form integrity with elastic hinges, is created by folding and weaving a shape-memory membrane, into a network of rigid members suspended with elastic hinges. The shape-shifting
From playlist G4G12 Videos
What is an Injective Function? Definition and Explanation
An explanation to help understand what it means for a function to be injective, also known as one-to-one. The definition of an injection leads us to some important properties of injective functions! Subscribe to see more new math videos! Music: OcularNebula - The Lopez
From playlist Functions
Functions, Domain, Codomain, Injective(one to one), Surjective(onto), Bijective Functions
Functions, Domain, Codomain, Injective(one to one), Surjective(onto), Bijective Functions All definitions given and examples of proofs are also given. Also discussed the intuition behind the definitions. Hope this makes sense:)
From playlist Functions, Sets, and Relations
Surjective, Injective, and Bijective Functions
This video introduces surjective, injective, and bijective functions.
From playlist Functions (Discrete Math)
Python Programming 18. Functions
This is the 18th in a course of computer science video lessons introducing programming with Python. This lesson explains the difference between a sub procedure and a function. You will learn that, by definition, a function is a sub program that returns a value to the program that called
From playlist Python Programming Step by Step
Definition of an Injective Function and Sample Proof
We define what it means for a function to be injective and do a simple proof where we show a specific function is injective. Injective functions are also called one-to-one functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear https://amzn.to/3BFvcxp (these are my affil
From playlist Injective, Surjective, and Bijective Functions
Combining Algos with a Vote - Natural Language Processing With Python and NLTK p.16
Now that we have many classifiers, what if we created a new classifier, which combined the votes of all of the classifiers, and then classified the text whatever the majority vote was? Turns out, doing this is super easy. NLTK has considered this in advance, allowing us to inherit from t
From playlist NLTK with Python 3 for Natural Language Processing
AI creates Image Classifiers…by DRAWING?
In this video, we talk about "Sketch-a-Classifier" released by researchers at the university of London. KEYWORDS 1. Zero Shot Learning 2. Model Regression Networks (MRN) 3. Parametric Model 4. Multilayer Perceptron (MLP) 5. Fully Convolutional Network (FCN) 6. Regression Loss 7. Performa
From playlist Deep Learning Research Papers
Injective(one-to-one), Surjective(onto), Bijective Functions Explained Intuitively
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys A nice way to think about injective(one-to-one), surjective(onto), and bijective functions.
From playlist Functions, Sets, and Relations