Category theory | Algebraic topology
Given a size pair where is a manifold of dimension and is an arbitrary real continuous function definedon it, the -th size functor, with , denoted by , is the functor in , where is the category of ordered real numbers, and is the category of Abelian groups, defined in the following way. For , setting , , equal to the inclusion from into , and equal to the morphism in from to , * for each , * In other words, the size functor studies theprocess of the birth and death of homology classes as the lower level set changes.When is smooth and compact and is a Morse function, the functor can bedescribed by oriented trees, called − trees. The concept of size functor was introduced as an extension to homology theory and category theory of the idea of size function. The main motivation for introducing the size functor originated by the observation that the size function can be seen as the rankof the image of . The concept of size functor is strictly related to the concept of , studied in persistent homology. It is worth to point out that the -th persistent homology group coincides with the image of the homomorphism . (Wikipedia).
Micrometer/diameter of daily used objects.
What was the diameter? music: https://www.bensound.com/
From playlist Fine Measurements
Chapter 5 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Chapter 1 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Vernier caliper / diameter and length of daily used objects.
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From playlist Fine Measurements
How big are complex numbers? We discuss a way of measuring them via the modulus. The ideas use Pythagorus' theorem. Free ebook http://bookboon.com/en/introduction-to-complex-numbers-ebook
From playlist Intro to Complex Numbers
Chapter 6 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Micrometer / diameter of daily used objects
What was the diameter? music: https://www.bensound.com/
From playlist Fine Measurements
Another practice problem dealing with the volume of a sphere
From playlist Middle School - Worked Examples
Higher Algebra 7: Non-abelian derived functors
In this video, we discuss the notion of non-abelian derived functors and Animation. Along the way, we discuss the Yoneda lemma. Warning: The Yoneda exercises stated at 35:00 is a bit hard given the technology we have, so I recommend simply proving the analogous statement for ordinary cat
From playlist Higher Algebra
Martina Scolamiero 9/15/21: Extracting persistence features with hierarchical stabilisation
Title: Extracting persistence features with hierarchical stabilisation Abstract: It is often complicated to understand complex correlation patterns between multiple measurements on a dataset. In multi-parameter persistence we represent them through algebraic objects called persistence mo
From playlist AATRN 2021
Serge Bouc: Correspondence functors
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
Emily Riehl: On the ∞-topos semantics of homotopy type theory: The simplicial model of...- Lecture 2
HYBRID EVENT Recorded during the meeting "Logic and Interactions" the February 22, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual M
From playlist Topology
Justin Lynd: Control of fixed points and centric linking systems
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: Workshop "Fusion systems and equivariant algebraic topology"
From playlist HIM Lectures: Junior Trimester Program "Topology"
An introduction to the process of finding the volume of a sphere
From playlist Middle School - Worked Examples
Sejong Park: Double Burnside rings and Mackey functors with applications to fusion systems
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: Workshop "Fusion systems and equivariant algebraic topology"
From playlist HIM Lectures: Junior Trimester Program "Topology"
Ivan Di Liberti - Towards higher topology
Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/DiLibertiSlidesToposesOnline.pdf We categorify the adjunction between locales and topological spaces, this amounts t
From playlist Toposes online
Emily Riehl: On the ∞-topos semantics of homotopy type theory: All ∞-toposes have... - Lecture 3
HYBRID EVENT Recorded during the meeting "Logic and Interactions" the February 24, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual M
From playlist Topology
Paul Turner: A hitchhiker's guide to Khovanov homology - Part II
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Geometry
Dimensions (2 of 3: A More Flexible Definition - Scale Factor)
More resources available at www.misterwootube.com
From playlist Exploring Mathematics: Fractals
Yonatan Harpaz - New perspectives in hermitian K-theory III
For questions and discussions of the lecture please go to our discussion forum: https://www.uni-muenster.de/TopologyQA/index.php?qa=k%26l-conference This lecture is part of the event "New perspectives on K- and L-theory", 21-25 September 2020, hosted by Mathematics Münster: https://go.wwu
From playlist New perspectives on K- and L-theory