symmetric monoidal (∞,1)-category of spectra
categorification
Just as a groupoid is the oidification of a group and a ringoid is the oidification of a ring, a quasigroupoid should be the oidification of a quasigroup.
A quasigroupoid is a magmoid $Q$ such that for every span
in $Q$, there exists morphisms $i:x\to y$ and $j:y \to x$ such that $i \circ f = g$ and $j \circ g = f$, and for every cospan
in $Q$, there exists morphisms $d:a\to b$ and $e:b \to a$ such that $g \circ d = f$ and $f \circ e = g$.
Every groupoid is a quasigroupoid.
Every loopoid and associative quasigroupoid is a quasigroupoid.
A one-object quasigroupoid is a quasigroup.
A quasigroupoid enriched in truth values is an equivalence relation.
Last revised on November 14, 2022 at 14:58:42. See the history of this page for a list of all contributions to it.