Item 1 (001P) — The Clowder Project

Preferences





Font:

PDF Style:

Here's a breakdown of the differences between each PDF style:

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`

*To be replaced with Linus Romer's Elemaints when it is released.

Associativity. We have isomorphisms of sets¹

\[ \underbrace{\text{Eq}\webleft (f\circ \text{eq}\webleft (g,h\webright ),g\circ \text{eq}\webleft (g,h\webright )\webright )}_{{}=\text{Eq}\webleft (f\circ \text{eq}\webleft (g,h\webright ),h\circ \text{eq}\webleft (g,h\webright )\webright )}\cong \text{Eq}\webleft (f,g,h\webright ) \cong \underbrace{\text{Eq}\webleft (f\circ \text{eq}\webleft (f,g\webright ),h\circ \text{eq}\webleft (f,g\webright )\webright )}_{{}=\text{Eq}\webleft (g\circ \text{eq}\webleft (f,g\webright ),h\circ \text{eq}\webleft (f,g\webright )\webright )}, \]

where $\text{Eq}\webleft (f,g,h\webright )$ is the limit of the diagram

in $\mathsf{Sets}$, being explicitly given by

\[ \text{Eq}\webleft (f,g,h\webright )\cong \webleft\{ a\in A\ \middle |\ f\webleft (a\webright )=g\webleft (a\webright )=h\webleft (a\webright )\webright\} . \]

Noticed something off, or have any comments? Feel free to reach out!

You can also use the contact form below: