Subsubsection 6.2.5.5 (00KP): The Associators

Style	Class	Font	Theorem Environments
Style 1	`book`	Alegreya Sans	`tcbthm`
Style 2	`book`	Alegreya Sans	`amsthm`
Style 3	`book`	Arno*	`amsthm`
Style 4	`book`	Computer Modern	`amsthm`

Style

Class

Font

Theorem Environments

Style 1

book

Alegreya Sans

tcbthm

Style 2

book

Alegreya Sans

amsthm

Style 3

book

Arno*

amsthm

Style 4

book

Computer Modern

amsthm

For each composable triple

\[ A\mathbin {\overset {R}{\mathrel {\rightarrow \kern -9.5pt\mathrlap {|}\kern 6pt}}}B\mathbin {\overset {S}{\mathrel {\rightarrow \kern -9.5pt\mathrlap {|}\kern 6pt}}}C\mathbin {\overset {T}{\mathrel {\rightarrow \kern -9.5pt\mathrlap {|}\kern 6pt}}}D \]

of horizontal morphisms of $\mathsf{Rel}^{\mathsf{dbl}}$, the component

of the associator of $\mathsf{Rel}^{\mathsf{dbl}}$ at $\webleft (R,S,T\webright )$ is the identity inclusion¹

¹This is justified by Chapter 7: Constructions With Relations, Item 2 of Proposition 7.3.12.1.3.

The Clowder Project

6.2.5.5 The Associators