The Aperiodical Mathematical Objects: An object with Tai-Danae Bradley
Dec 6, 2024
Tai-Danae Bradley, an expert in category theory and creator of the blog Mathema, joins the discussion to explore the significance of 'objects' in mathematics. They dive into category theory, using engaging examples like the Rubik's Cube to illustrate relationships between mathematical entities. The conversation highlights the composability of functions, the links between algebra and topology, and the beautiful connections between mathematics and reality, showcasing how abstract concepts find practical applications in the world.
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Objects in Category Theory
- In category theory, an object isn't simply a collection of items like a collage of podcast objects.
- It represents a collection of things sharing a common structure and their relationships.
Real Numbers and Group Theory
- Tai-Danae Bradley uses real numbers with addition as an example of group theory objects and their relationships.
- The function adding 1 to a real number doesn't preserve the structure, so it is not a group homomorphism.
Compositionality in Category Theory
- Category theory differs from graph theory because it emphasizes compositionality.
- Arrows, or morphisms, can be composed to create new arrows that respect the object's structure.
