# crumbs!

Physicist Freeman Dyson once observed that there are two types of mathematicians: birds -- those who fly high, enjoy the big picture, and look for unifying concepts -- and frogs -- those who dwell on the ground, find beauty in the scenery close by, and enjoy the details.

Of course, both vantage points are essential to mathematical progress, and I often tend to think of myself as more of a bird.(I'm, uh, bird-brained?)

# Group Elements, Categorically

On Monday we concluded our mini-series on basic category theory with a discussion on natural transformations and functors. This led us to make the simple observation that the elements of any set are really just functions from the single-point set {✳︎} to that set. But what if we replace "set" by "group"? Can we view group elements categorically as well? The answer to that question is the topic for today's post, written by guest-author Arthur Parzygnat

# What is a Natural Transformation? Definition and Examples, Part 2

Continuing our list of examples of natural transformations, here is Example #2 (double dual space of a vector space) and Example #3 (representability and Yoneda's lemma).

# What is a Natural Transformation? Definition and Examples

I hope you have enjoyed our little series on basic category theory. (I know I have!) This week we'll close out by chatting about natural transformations which are, in short, a nice way of moving from one functor to another. If you're new to this mini-series, be sure to check out the very first post, What is Category Theory Anyway? as well as What is a Category? and last week's What is a Functor?