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 unital magmoid should be the oidification of a unital magma.
A unital magmoid $Q$ is a magmoid where every object $a \in Ob(Q)$ has an identity morphism $id_a: a \to a$, such that for any morphism $f:a \to b$, $f \circ id_a = f$, and for any morphism $g:c \to a$, $id_a \circ g = g$.
A unital magmoid is invertible if for every pair of objects $a,b \in Ob(Q)$ and for every morphism $f:a \to b$, there exists an inverse morphism $g:b \to a$ such that $f \circ g = id_b$ and $g \circ f = id_a$.
A groupoid is a unital magmoid.
A unital magmoid with only one object is called a unital magma.
A unital magmoid enriched on truth values is a preorder.
Last revised on June 7, 2022 at 21:21:25. See the history of this page for a list of all contributions to it.