Proposed title : Do You Even Lift ?

Roots in algebraic topology in the early 1940s by Eilenberg and Mac Lane

It features strong abstractions and attempts to unify separate ideas.

It can translate difficult problems to easy ones.

It provides a powerful language .

A continuous function from a unit circle to itself must have a fixed point.

Brouwer's Theorem assures existence of equilibria in Game Theory.

Brouwer's Theorem assures existence of solutions to some differential equations.

After sloshing around a cup of coffee, at least one point will always remain in the same spot.

If you crumple up one sheet of paper and place it on top of a flat sheet, then at least one point will be directly over it's corresponding point.

h: D → S that leaves each point on S fixed.

Lemma : There is no continuous function

Let S be the surface of the unit-circle.

Let D be the unit-circle disk.

Using a Functor, we can transform one Category to another by preserving identities and compositions.

Proof of Lemma (Step 3)

By instead examining the Category of Groups, we can conclude that no such group homomorphism g: 0 → Z can exist.

We have proved the Lemma.