>>274
>しかし、それならそれで、従来の圏論との差分をとった説明がほしいよね
>従来の圏論と、この部分は同じだが、この部分が違うとか

圏論と言っても種類が多数あるらしい
まあ、IUTに一番近いと思われる圏を選んで対比するのが良いと思う

https://en.wikipedia.org/wiki/Outline_of_category_theory
Outline of category theory
(抜粋)
The following outline is provided as an overview of and guide to category theory, the area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows
(also called morphisms, although this term also has a specific, non category-theoretical sense), where these collections satisfy certain basic conditions.
Many significant areas of mathematics can be formalised as categories, and the use of category theory allows many intricate and subtle mathematical results in these fields to be stated, and proved, in a much simpler way than without the use of categories.

Contents
1 Essence of category theory
2 Branches of category theory
3 Specific categories
4 Objects
5 Morphisms
6 Functors
7 Limits
8 Additive structure
9 Dagger categories
10 Monoidal categories
11 Cartesian closed category
12 Structure
13 Topoi, toposes
14 History of category theory
15 Persons influential in the field of category theory

Essence of category theory
Category ?
Functor ?
Natural transformation ?

Branches of category theory
Homological algebra ?
Diagram chasing ?
Topos theory ?
Enriched category theory ?
Higher category theory ?

Additive structure
Derived category ?
Triangulated category ?
Model category ?
2-category ?

Cartesian closed category
Topos

Topoi, toposes
Sheaf ?
Gluing axiom ?
Descent (category theory) ?
Grothendieck topology ?