wedge sum (changes)

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We can stick~~ to~~ two spaces together by their points.

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? $\mathrm{in}:A+B\to AveeB\vee B$ in : A + B \to A
~~\veeB~~\vee B - 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 $\star_{A \vee B} \equiv \mathrm{inl}(\star_A)$

category: homotopy theory

Last revised on January 19, 2019 at 10:54:32. See the history of this page for a list of all contributions to it.