homotopy theory, (∞,1)-category theory, homotopy type theory
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symmetric monoidal (∞,1)-category of spectra
The oidification of an “H-magma”, which is to magmas what H-spaces are to unital magmas.
A H-magmoid is a 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, an H-magmoid $A$ consists of the following.
A type $A_0$, whose elements are called objects. Typically $A$ is coerced to $A_0$ in order to write $x:A$ for $x:A_0$.
For each $a,b:A$, a type $hom_A(a,b)$, whose elements are called arrows or morphisms.
For each $a,b,c:A$, a function
called composition, and denoted infix by $g \mapsto f \mapsto g \circ f$, or sometimes $gf$.
Last revised on June 7, 2022 at 21:41:28. See the history of this page for a list of all contributions to it.