Why should a combinatorialist know category theory?

Solution 1:

If you are interested in becoming a pioneer in a new area of mathematics that involves combinatorics then there is Combinatorial category theory.

László Lovász talks about this in a video interview starting at 1m59s in https://simonsfoundation.org/science_lives_video/laszlo-lovasz/?chapter=22

Also in his book Large networks and graph limits, chapter 23, http://www.cs.elte.hu/~lovasz/bookxx/hombook-oct-2012.pdf, there is a section on categories in which he says: "In graph theory, the use of categories (as a language and also as guide for asking question in a certain way) has been practiced mainly by the Prague school, and has lead to many valuable results; see e.g. the book by Hell and Nešetřil [2004]." (Graphs and Homomorphisms)

The dual space of $c$ is $\ell^1$

Prerequisites for functional analysis

"Sum equals integral" identities similar to $\int_0^1 \frac{dx}{x^x} = \sum_{n = 1}^{\infty} \frac{1}{n^n}$

When does the boundary have measure zero?

Points in plane with every pair having at least two equidistant points?

Nice way of thinking about the Laplace operator... but what's the proof?

What are the applications of finite calculus

Existence of an holomorphic function

Evaluate the infinite product $\prod_{k \geq 2}\sqrt[k]{1+\frac{1}{k}}=\sqrt{1+\frac{1}{2}} \sqrt[3]{1+\frac{1}{3}} \sqrt[4]{1+\frac{1}{4}} \cdots$

Finding properties of operation defined by $x⊕y=\frac{1}{\frac{1}{x}+\frac{1}{y}}$? ("Reciprocal addition" common for parallel resistors)

A prime number random walk

is it possible to motivate higher differential forms without integration?