Category Theory Illustrated – Orders
by boris_m on 4/18/2026, 6:40:47 AM
https://abuseofnotation.github.io/category-theory-illustrated/04_order/
Comments
by: dgan
I think it is pretty obvious that at the challenge with all abstract mathematics in general and the category theory in particular isnt the fact that people dont understand what a "linear order" is, but the fact it is so distant from daily routine that it seems completely pointless. It's like pouring water over pefectly smooth glass
4/18/2026, 8:00:59 AM
by: arketyp
There is a way to frame category theory such that <i>it's all just arrows</i> -- by associating the identity arrow (which all objects have by definition) with the object itself. In a sense, the object is syntactic sugar.
4/18/2026, 7:59:11 AM
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4/18/2026, 8:22:55 AM
by: gobdovan
Unless there's some idiosyncratic meaning for the `=>`, the Antisymmetry one basically says `Orange -> Yellow => Yellow -/> Orange`. The diagram is not acurate. The prose is very imprecise. "It also means that no ties are permitted - either I am better than my grandmother at soccer or she is better at it than me." NO. Antisymmetry doesn't exclude `x = y`. Ties are permitted in the equality case. Antisymmetry for a non-strict order says that if both directions hold, the two elements must in fact be the same element. The author is describing strict comparison or total comparability intuition, not antisymmetry.
4/18/2026, 8:26:05 AM
by: somewhereoutth
The first 90% of this is standard set theory.<p>I'm unclear what the last 10% of 'category theory' gives us.
4/18/2026, 8:41:46 AM