Why should a combinatorialist know category theory?

Question

I know almost nothing about category theory (I have just skimmed the first chapters of Aluffi's algebra book), reading this question got me thinking... why should someone mostly interested in combinatorics/graph theory learn category theory?

What I am asking for is examples of how knowledge of category theory might be beneficial for someone doing combinatorics.

You might be interested in combinatorial species, which are most naturally described as an endofunctor on the category of finite sets and bijections. — Chris Taylor, Apr 05 '13 at 11:04
I've posted a "follow-up" question about combinatorial species here — Carolus, Apr 06 '13 at 04:44

score 15 · Answer 1 · answered Apr 06 '13 at 06:20

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)

Apparently an update for the second link, which is dead: http://www.cs.elte.hu/~lovasz/bookxx/hombook-almost.final.pdf — darij grinberg, May 03 '15 at 05:10

score 0 · Answer 2 · answered Jun 10 '16 at 00:13

0

You might find interesting Extensive categories and the size of an orbit by Ernie Manes (TAC, 2015).

answered Jun 10 '16 at 00:13

Keith Harbaugh

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Why should a combinatorialist know category theory?

2 Answers2

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