Pseudonium

Definition by Doing The main idea I’ve wanted to emphasise again and again in this “Baby Yoneda” series is the concept of is-does duality: The Yoneda Lemma is the statement that “what something is is equivalent to what something does”.

Packaging Monotone Maps Before releasing the next article in the “Baby Yoneda” series, I want to do another exploration in a similar style to Discovering Topological Products, but this time for products of ordered sets.

Packaging Objects In the previous article, we looked at virtual objects and their representations in more detail.

Matching Blueprints Before embarking on a large construction project, it helps to have a blueprint of the structure you want to build.

Following The Identity In quite a few of my recent articles, we’ve used this trick of “following the identity”.

Intersecting Problems In my recent article on Why Preimages Preserve Subset Operations, I explained that taking preimages of subsets can be viewed simply as function composition with predicates.

Preimages beat Images Soon after being introduced to sets and functions, you might come across the notion of the image and preimage of a subset.

A Pointwise Puzzle Here’s a question from my undergrad which was much harder than I anticipated at the time: Let $X$ be a topological space, and $f, g : X \to \mathbb{R}$ be continuous functions.

Packaging Objects The modern foundations of mathematics are set theory, most commonly ZFC.

The Axiom of Choice There are a few equivalent versions of the Axiom of Choice, with Zorn’s Lemma and the Well-Ordering Principle being the most popular examples.