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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.

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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 5 '13 at 11:04
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Not beneficial. Forget it. –  Berci Apr 5 '13 at 11:07
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@Berci: could you elaborate on your rather cryptic comment? –  Rasmus Apr 5 '13 at 11:18
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Refer to Chris Taylor's comment on combinatorial species. –  Zhen Lin Apr 5 '13 at 14:54
    
I've posted a "follow-up" question about combinatorial species here –  Carolus Apr 6 '13 at 4:44

1 Answer 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)

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Interesting. I will look into this, definitely! –  Carolus Apr 6 '13 at 6:25

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