2025-09-26
This following is a very brief summary of what happened in class on 2025-09-26.
We began by recapping a universal property of the quotient module construction. I made the claim that this property uniquely characterizes the morphism
We then explored the idea of a "universal property" for other constructions, looking at several other examples, some familiar and others less so. We will return to this idea several times over the next few weeks, gradually filling in the details (including eventually a precise, formal definition for "universal property").
Concepts
Quotient modules
The Isomorphism Theorems for Modules
Universal Properties I - Inspiring Examples
References
- Dummit & Foote, Abstract Algebra: Section 10.2
- Mac Lane, Categories for the Working Mathematician: pp. 13-15