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H-spaces Sometimes are we simply can types equip equipped with the structure of a magma (from classical Algebra). They are useful classically in constructing fibrations.type with a certain structure, called a H-space, allowing us to derive some nice properties about the type or even construct fibrations
A H-Space consists ofH-Space consists of
Let $A$ be a connected H-space. Then for every$a:A$connected? , the H-space. maps Then for every$\mu (a,-),\mu (-,a):A\to A$ \mu(a,-),\mu(-,a):A a:A \to A , are the equivalences.maps? $\mu(a,-),\mu(-,a):A \to A$ are equivalences?.
There is a H-space structure on the circle. See Lemma 8.5.8 of the HoTT book. (TODO: Write out construction).
Every loop space is naturally a H-space with path concatenation as the operation. In fact every loop space is a group?.
The type of maps? $A \to A$ has the structure of a H-space, with basepoint $id_A$, operation function composition.
Synthetic homotopy theory hopf fibration
Classically, an H-space is a homotopy type equipped with the structure of a unital magma in the homotopy category (only).
Revision on January 1, 2019 at 20:51:23 by Ali Caglayan. See the history of this page for a list of all contributions to it.