スザウィール論文からの引用

スタニスワフ・スザウィール〈Stanisław Szawiel〉はおそくらポーランド人。ワルシャワ大学出身。

• Title: A Unified Approach to Opetopic Algebra
• Author: Stanisław Szawiel
• Pages: 197
• URL: https://depotuw.ceon.pl/bitstream/handle/item/1115/doktorat.pdf

p.7

In short, understanding category theory starts with a 2-category. This pattern repeats itself indefinitely: to understand the mentioned universal constructions in Cat properly, one needs to work with 3-categories. In general, the understanding of n-categories requires knowledge of (n + 1)-categories. The internal consistency of category theory demands the development of higher categories.

p.25

Set-theoretic assumptions. We postulate two Grothendieck universes U₁, U₂, such that U₁ ∈ U₁. We let Set be the category of sets in U1 and Cat be the 2-category of categories in U2. Therefore we may write Set ∈ Cat. We shall suppress the U_i from notation. All required notions of smallness will be clear from their context. All the results about specific categories in this work may be proven without recourse to Grothendieck universes. Doing so, however, would result in a complete loss of conceptual clarity.