Explore the Endless Possibilities of Categories

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The discussion centers on the concept of categories in category theory, highlighting the existence of an infinite number of categories and their properties. Key topics include the definitions of fully faithful functors, contravariant functors, and the nuances of Baez's concept of *-categories. Participants explore the implications of these definitions and their relationships, while also debating the criteria for distinguishing different kinds of categories. The conversation reflects a deep engagement with foundational concepts in category theory, emphasizing the complexity and richness of the subject.
  • #31
If objects can be replaced between categories, do we get mathematical structures that can be ordered by their abilities to replace objects, and if so, how this CAT structure will look like?
 
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  • #32
Your last post looks like something that organic would post and makes no sense at all so I correspondenigly refuse to answer it.
 
  • #33
I'm wondering if there exist a category in which the objects are tensors; if this category exist, please what's its name and what morphisms it has.
 
  • #34
Whilst there are tensor categories you ought to bear in mind these tensors are not the tensors I'm guessing you know about (invariant under rotation), so don't be mislead.
 

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