@abuseofnotation There are at least two reasons that categories aren't usually covered during an introduction to abstract algebra.

1) While the modern upper-level undergraduate curriculum does push a lot more abstraction than appeared a century ago, this is still balanced with the psychological need for students to not go up too many levels too quickly. Even though categories are some kind of algebraic structure generalizing groups and lattices, the standard examples are categories of other mathematical objects one has already studed (sets, groups, etc.). For students this is conceptually quite different from the more concrete situation of finite symmetry groups, for example.

2) The applications of categories (separately from the special cases of groups/lattices/monoids/posets/etc.) don't yet appear enough for the average person with a bachelor's in math to need to know them. This may change as #AppliedCategoryTheory, #TopologicalDataAnalysis, #FunctionalProgramming, and so forth continue to mature and have greater impacts outside of academia.

3/

The authors provide important definitions and theorems on critical edges, local minima, and selective Rips complexes, and caution that certain assumptions are necessary for their results to hold. #Topology #RipsComplexes #PersistentHomology #ComputerScience #TopologicalDataAnalysis

https://arxiv.org/pdf/2304.05185.pdf

For @3CardMonteCarloMethodMan

Thanks for the follow David.

The fifth #collage is for you.

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