2-category

2-category

of Cat- category theory; and it cuts through some of the technical nightmares of bicategories. The prefix “ 2 -”, as in 2 -functor or 2 -limit, will always denote the strict.
Guest post by Dimitri Zaganidis. First of all, I would like to thank Emily for organizing the Kan extension seminar. It is a pleasure to be part of it.
In category theory, a 2 - category is a category with "morphisms between morphisms"; that is, where each hom-set itself carries the structure of a category.

2-category - phone number

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Well, nice to meet you, Dimitris. 2-category, you're right, the localizations are the adjunctions with exact left adjoints. Read the post An Exegesis of Yoneda Structures. Enter your comment here. 2-category it has a collection of objects, and for each 2-category of objects a category hom xy hom x,y. I think the "natural" notion of homomorphism that arises this way is that of a profunctor rather than a functor, but that should be considered a feature rather than a bug. This is a category 2 pair vs straight in the category of groups.