Bruno Marchal in an older post wrote:
>> Also,
>> can you elaborate a bit more on the motivation behind category theory?
>> Why
>> was it invented, and what problems does it solve? What's the relationship
>> between category theory and the idea that all possible universes exists?
> 
> 
> Tim makes a very genuine remark (but he writes so much I fear that has
> been unnoticed!). He said: read Tegmark (Everything paper), then learn
> category, then read again Tegmark. Indeed I would say category theory has

Bruno, which of the Tegmark's 'Everything papers' did you have in your mind?

> emerged from the realisation that mathematical structures are themselves
> mathematically structured. Categorist applies the every-structure principle
> for each structure. Take all groups, and all morphism between groups: you
> get the category of groups. It is one mathematical structure, a category
> (with objects = groups and arrows = homomorphism) which, in some sense
> capture the essence of group.

Cheers,
 mirek

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