Explore >> Select a destination
|
You are here 
|
leanprover-community.github.io | ||
| | | | |
lucatrevisan.wordpress.com
|
|
| | | | | In which we show how to find the eigenvalues and eigenvectors of Cayley graphs of Abelian groups, we find tight examples for various results that we proved in earlier lectures, and, along the way, we develop the general theory of harmonic analysis which includes the Fourier transform of periodic functions of a real variable, the... | |
| | | | |
ncatlab.org
|
|
| | | | | [AI summary] The Dold-Kan correspondence is a fundamental result in algebraic topology and homological algebra that establishes an equivalence between the category of simplicial abelian groups and the category of non-negatively graded chain complexes of abelian groups. This correspondence allows for the translation of problems between these two frameworks, facilitating the study of homotopy theory and homological algebra. Key aspects include its role in constructing Eilenberg-MacLane spaces, looping and delooping operations, and its applications in sheaf cohomology and computational methods. The correspondence is rooted in the work of Dold and Kan and has been generalized to various contexts, including semi-Abelian categories and stable homotopy theory. | |
| | | | |
www.jeremykun.com
|
|
| | | | | The First Isomorphism Theorem The meat of our last primer was a proof that quotient groups are well-defined. One important result that helps us compute groups is a very easy consequence of this well-definition. Recall that if $ G,H$ are groups and $ \varphi: G \to H$ is a group homomorphism, then the image of $ \varphi$ is a subgroup of $ H$. Also the kernel of $ \varphi$ is the normal subgroup of $ G$ consisting of the elements which are mapped to the identity under $ \varphi$. | |
| | | | |
francisbach.com
|
|
| | | |||
