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Category Theory as far as I understood is about how objects are related to each other.

So why do we then consider "directed" morphisms rather then "undirected" ones?

I mean for example relations between sets rather than maps between sets as these are more general. Sure, plain relations can be covered within the category approach too but goin the other way around would be more plausible.

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To only have to check half as much when verifying commutativity of a diagram? :-) – Eric Towers Mar 10 '14 at 9:29
I mean, it is because category theory is the study of relation by structure preserving maps. Maps are directed. – Alex Youcis Mar 10 '14 at 9:30
Have you had a look at allegories? I mean, not that binary relations wouldn’t define arrows as well. Binary relations are directed. – k.stm Mar 10 '14 at 9:31
Also relations are directed, so you still need an arrow. – magma Mar 10 '14 at 9:34
Aaahhh =D you're right relations are directed too ...thx man thats it =D ...can u post this as answer? – Alexander Frei Mar 10 '14 at 10:14
up vote 0 down vote accepted

Since even relations can be expressed as arrows could in principle also define relations as unordered pairs however they always simultaneously are given as ordered pairs so there's no gain in doing so

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