# Homotopy Type Theory wedge sum (Rev #4, changes)

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## Idea

The We wedge can sum stick of to two spaces types together by their points.$A$ and $B$, can be defined as the pushout of the span

$A \leftarrow \mathbf{1} \rightarrow B$

where the maps pick the base points of $A$ and $B$. This pushout is denoted $A \vee B$ and has basepoint $\star_{A \vee B} \equiv \mathrm{inl}(\star_A)$

## Definition

The wedge sum of two pointed types $(A,a)$ and $(B,b)$ can be defined as the higher inductive type with the following constructors:

• Points come from the sum type? $in : A + B \to A \veeB$
• And their base point is glued $path : inl(a) = inr(b)$ Clearly this is pointed.

The wedge sum of two types $A$ and $B$, can also be defined as the pushout of the span

$A \leftarrow \mathbf{1} \rightarrow B$

where the maps pick the base points of $A$ and $B$. This pushout is denoted $A \vee B$ and has basepoint $\star_{A \vee B} \equiv \mathrm{inl}(\star_A)$

## References

HoTT book

category: homotopy theory

Revision on January 19, 2019 at 10:54:06 by Ali Caglayan. See the history of this page for a list of all contributions to it.