Proposition 4.3.2.1.2 (00B3): Properties of Coproducts of Families of Pointed Sets

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.

Table of Contents
Part 1: Sets
Chapter 4: Pointed Sets
Section 4.3: Colimits of Pointed Sets
Subsection 4.3.2: Coproducts of Families of Pointed Sets
Proposition 4.3.2.1.2: Properties of Coproducts of Families of Pointed Sets (cite)

Let ${(X_{i}, x_{0}^{i})}_{i \in I}$ be a family of pointed sets.

1. Functoriality. The assignment ${(X_{i}, x_{0}^{i})}_{i \in I} \mapsto (\underset{i \in I}{⋁} X_{i}, p_{0})$ defines a functor
$\underset{i \in I}{⋁} : Fun (I_{disc}, {Sets}_{*}) \to {Sets}_{*} .$

Proof of Proposition 4.3.2.1.2.

Item 1: Functoriality

This follows from

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

You can also use the contact form below: