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 magmoid should be the oidification of a magma.
Let be a quiver with a collection of objects , a set of morphisms , a function called the source or domain and a function called the target or codomain. A magmoid is a quiver with a partial binary operation
with coproduct injections and , such that for , there is a function in the inverse image of if , and otherwise.
Let be a quiver with a collection of objects and a Set-valued functor for all objects . A magmoid is a quiver with a binary operation
for all .
A weak magmoid is a magmoid whose collection of objects form a groupoid, while a strict magmoid is a magmoid whose collection of objects form a set.
Let be a monoidal category (or a monoidal (infinity,1)-category) and let be a -enriched quiver, with a collection of objects and a -valued functor for all objects . A -enriched magmoid is a -enriched quiver with a binary operation
for all .
A transitive relation is a magmoid enriched in truth values, or a magmoid where there is at most one morphism from every object to another object in .
Last revised on January 20, 2023 at 04:00:55. See the history of this page for a list of all contributions to it.