Morphisms | Algebraic properties of elements
In category theory, an epimorphism (also called an epic morphism or, colloquially, an epi) is a morphism f : X → Y that is right-cancellative in the sense that, for all objects Z and all morphisms g1, g2: Y → Z, Epimorphisms are categorical analogues of onto or surjective functions (and in the category of sets the concept corresponds exactly to the surjective functions), but they may not exactly coincide in all contexts; for example, the inclusion is a ring epimorphism. The dual of an epimorphism is a monomorphism (i.e. an epimorphism in a category C is a monomorphism in the dual category Cop). Many authors in abstract algebra and universal algebra define an epimorphism simply as an onto or surjective homomorphism. Every epimorphism in this algebraic sense is an epimorphism in the sense of category theory, but the converse is not true in all categories. In this article, the term "epimorphism" will be used in the sense of category theory given above. For more on this, see below. (Wikipedia).
Category Theory 2.2: Monomorphisms, simple types
Monomorphisms, simple types.
From playlist Category Theory
Homomorphisms in abstract algebra
In this video we add some more definition to our toolbox before we go any further in our study into group theory and abstract algebra. The definition at hand is the homomorphism. A homomorphism is a function that maps the elements for one group to another whilst maintaining their structu
From playlist Abstract algebra
There are two different types of reductionism. One is called methodological reductionism, the other one theory reductionism. Methodological reductionism is about the properties of the real world. It’s about taking things apart into smaller things and finding that the smaller things determ
From playlist Philosophy of Science
What are Connected Graphs? | Graph Theory
What is a connected graph in graph theory? That is the subject of today's math lesson! A connected graph is a graph in which every pair of vertices is connected, which means there exists a path in the graph with those vertices as endpoints. We can think of it this way: if, by traveling acr
From playlist Graph Theory
Being a victim of infidelity is one of the worst things that can befall us in love. One of the ways to come back from the harrowing experience is to ask what the real meaning of the infidelity might be. If you like our films, take a look at our shop (we ship worldwide): https://goo.gl/yW1
From playlist RELATIONSHIPS
This lecture is part of an online course on Category theory This is the introductory lecture, where we give a few examples of categories and define them. The lectures were originally part of a graduate algebra course, and give a quick overview of the basic category theory that is useful
From playlist Categories for the idle mathematician
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Welcome to Shadows of Computation, an online course taught by Will Troiani and Billy Snikkers, covering the foundations of category theory and how it is used by computer scientists to abstract computing systems to reveal their intrinsic mathematical properties. In the third lecture Will sp
From playlist Shadows of Computation
The dynamics of Aut(Fn) actions on group presentations and representations - Alexander Lubotzky
Character Varieties, Dynamics and Arithmetic Topic: The dynamics of Aut(Fn) actions on group presentations and representations Speaker: Alexander Lubotzky Affiliation: Hebrew University of Jerusalem; Visiting Professor, School of Mathematics Date: December 15, 2021 Several different area
From playlist Mathematics
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This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
The idea of ‘atonement’ sounds very old-fashioned and is deeply rooted in religious tradition. To atone means, in essence, to acknowledge one’s capacity for wrongness and one’s readiness for apology and desire for change. It’s a concept that every society needs at its center. For gifts and
From playlist RELATIONSHIPS
How Is the ADHD Brain Different?
If you’re online, you may notice that conversations around ADHD are everywhere. You may even be starting to wonder, as you flick from one app to the next, that you yourself may have ADHD. So in Part 1 of this series about ADHD, Julian explores what this disorder is, what’s happening in the
From playlist Seeker+
Epimorphic Image of a Normal Subgroup Proof
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Epimorphic Image of a Normal Subgroup Proof. Given an epimorphism from G to K if H is a normal subgroup of G then the direct image of H is a normal subgroup of K.
From playlist Abstract Algebra
Étale cohomology lecture 3, August 27, 2020
Sites and sheaves, the étale and fppf site, representable functors
From playlist Étale cohomology and the Weil conjectures
Stability and Invariant Random Subgroups - Henry Bradford
Stability and Testability Topic: Stability and Invariant Random Subgroups Speaker: Henry Bradford Affiliation: Cambridge University Date: January 20, 2021 For more video please visit http://video.ias.edu
From playlist Stability and Testability
Markus Rosenkranz Talk 2 7/7/14 Part 1
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From playlist Spring 2014
Learn how to eliminate the parameter given sine and cosine of t
Learn how to eliminate the parameter in a parametric equation. A parametric equation is a set of equations that express a set of quantities as explicit functions of a number of independent variables, known as parameters. Eliminating the parameter allows us to write parametric equation in r
From playlist Parametric Equations
Nursultan Kuanyshov: Lusternik-Schnirelmann category of group homomorphism
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From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022