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In the Monster Group Definitely the Largest Finite Simple Group?
I just saw a post about the theorem of Classification of Finite Simple Groups and that the theorem has been formalized in Lean. But it dawned on me reading it that I always thought the Monster group was only the *known* largest finite simple group. Is it the case that it is actually *the largest* finite simple group, or could there be larger order ones?
#science
I just saw a post about the theorem of Classification of Finite Simple Groups and that the theorem has been formalized in Lean. But it dawned on me reading it that I always thought the Monster group was only the *known* largest finite simple group. Is it the case that it is actually *the largest* finite simple group, or could there be larger order ones?
#science
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rikagaku chalk in europe
Little off topic for the chalk snobs. A coworker told me about this chalk and said that they were quite good. Wanted to see what the hype was about. Are there any shops/sellers where you can get them for a reasonable price in Europe (more specifically Benelux/adjacent areas of germany/france)? Shipping fees from east asia are incredibly high, to a point where it's simply not worth it anymore for me.
#science
Little off topic for the chalk snobs. A coworker told me about this chalk and said that they were quite good. Wanted to see what the hype was about. Are there any shops/sellers where you can get them for a reasonable price in Europe (more specifically Benelux/adjacent areas of germany/france)? Shipping fees from east asia are incredibly high, to a point where it's simply not worth it anymore for me.
#science
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Why do people like contravariant functors more than covariant ones?
In most category theory texts and in applications I tend to observe that contravariance is given more page presence than covariant ones. What are the reasons behind this(if this is a valid observation)?
One reason I can think of is that in geometry people encounter contravariant functors more often than covariant ones.
Another reason is probably that letting your functors be contravariant let's you in turn have the embedding of the category into the functor category as covariant and hence this is a nice way of looking at objects of a category as functors.
#science
In most category theory texts and in applications I tend to observe that contravariance is given more page presence than covariant ones. What are the reasons behind this(if this is a valid observation)?
One reason I can think of is that in geometry people encounter contravariant functors more often than covariant ones.
Another reason is probably that letting your functors be contravariant let's you in turn have the embedding of the category into the functor category as covariant and hence this is a nice way of looking at objects of a category as functors.
#science