homotopy theory, (∞,1)-category theory, homotopy type theory
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symmetric monoidal (∞,1)-category of spectra
The oidification of an H-space.
A H-spaceoid is a unital magmoid internal to the classical homotopy category of topological spaces Ho(Top), or in the homotopy category $Ho(Top)_*$ of pointed topological spaces, which has a unit up to homotopy.
In homotopy type theory, a H-spaceoid is a type $A$ with
For each $a,b:A$, a type $hom_A(a,b)$, whose elements are called arrows or morphisms.
For each $a:A$, a morphism $1_a:hom_A(a,a)$, called the identity morphism.
For each $a,b,c:A$, a functor
called composition, and denoted infix by $g \mapsto f \mapsto g \circ f$, or sometimes $gf$.
For each $a,b:A$ and $f:hom_A(a,b)$, terms $p:f = 1_b \circ f$ and $q:f=f\circ 1_a$.
Last revised on June 7, 2022 at 21:40:55. See the history of this page for a list of all contributions to it.