記法の約束の例

https://www.academia.edu/28844867/Quantum_Kan_Extensions_and_Applications(ローカルにダウンロード済み)の記法の約束

Guide to Notation

New terms are underlined when defined. Bibliography citations appear in brackets such as [102]. Cross references are indicated with a chapter, section, subsection, or subsubsection number such as 2.811.
Sections are numbered sequentially in an alphanumeric format: 87.1, 87.2, . . . , 87.9, 87.a, . . . , 87.f, for example, indicate the first fifteen sections of chapter 87. Nesting of subsections and subsubsections is indicated with appended characters: 87.11, 87.12, . . . , 87.1a, 87.1b, . . . are subsections of 87.1 and 87.111, 87.112, . . . , 87.11a, . . . are subsubsections of 87.11. This concise notation is adapted from [69].

An assertion to be proved is not labeled as a theorem, lemma, or corollary, for example, but is typed in a slanted font:

3.122 $`{\bf Set}`$ is complete, hence, cartesian.

and is followed by a justification of the claim:

Because: it has equalizers and small products. ■

A black box at the right of a page indicates the end of a proof.

Naming of a category after its objects is indicated by the phrase: ‘category of . . . ’ (e.g. the category of sets) while naming after its morphisms is indicated by: ‘category composed of . . . ’ (e.g. the category composed of stochastic matrices).

可換(あるいは非可換)図式に関しては: