# nLab quasigroupoid

Contents

category theory

## Applications

#### Algebra

higher algebra

universal algebra

categorification

# Contents

## Idea

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.

## Definition

A quasigroupoid is a magmoid $Q$ such that for every span

$\array{ && s \\ & {}^{f}\swarrow && \searrow^{g} \\ x &&&& y }$

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

$\array{ && a &&&& b \\ & && {}_{f}\searrow & & \swarrow_g && \\ &&&& c &&&& }$

in $Q$, there exists morphisms $d:a\to b$ and $e:b \to a$ such that $g \circ d = f$ and $f \circ e = g$.

## Examples

Last revised on November 14, 2022 at 14:58:42. See the history of this page for a list of all contributions to it.