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Category: Category Theory

Applications of Reflections: Taking a Group to its “Abelian” Form

Applications of Reflections: Taking a Group to its “Abelian” Form

In continuing the exploration of explicit applications and examples of category-theoretic concepts, we highlight the versatility of reflections and reflective subcategories. This concept can be used to perform all kinds of desired actions on a category to yield a subcategory that "nicer" in some way. This article explores how we can use reflections to make…

Equivalence v. Isomorphisms in Category Theory

Equivalence v. Isomorphisms in Category Theory

Introduction Editor's Note: The article is co-written by Rachel Traylor (The Math Citadel/Marquette University) and Valentin Fadeev (The Open University, UK). Substantial additional review, contributions, and discussions were provided by Matt Kukla and Jason Hathcock. A pdf is available for download at the end of this post. The biggest challenge we have found in studying…