nLab flexible magmoid

Idea

Just as a groupoid is the oidification of a group and a ringoid is the oidification of a ring, an flexible magmoid should be the oidification of a flexible magma.

Definition

A flexible magmoid is a magmoid $Q$ such that for every two objects $a,b \in Ob(Q)$ and for every two morphisms $f:a \to b$ and $g:b \to a$,

$$f \circ (g \circ f) = (f \circ g) \circ f \,.$$

Examples

• Every category is a flexible magmoid.

• A one-object flexible magmoid is a flexible magma.

• A Mod-enriched flexible magmoid is called a flexible linear magmoid.

Related concepts

algebraic structure	oidification
magma	magmoid
pointed magma with an endofunction	setoid/Bishop set
unital magma	unital magmoid
quasigroup	quasigroupoid
loop	loopoid
semigroup	semicategory
monoid	category
anti-involutive monoid	dagger category
associative quasigroup	associative quasigroupoid
group	groupoid
flexible magma	flexible magmoid
alternative magma	alternative magmoid
absorption monoid	absorption category
cancellative monoid	cancellative category
rig	CMon-enriched category
nonunital ring	Ab-enriched semicategory
nonassociative ring	Ab-enriched unital magmoid
ring	ringoid
nonassociative algebra	linear magmoid
nonassociative unital algebra	unital linear magmoid
nonunital algebra	linear semicategory
associative unital algebra	linear category
C-star algebra	C-star category
differential algebra	differential algebroid
flexible algebra	flexible linear magmoid
alternative algebra	alternative linear magmoid
Lie algebra	Lie algebroid
monoidal poset	2-poset
strict monoidal groupoid?	strict (2,1)-category
strict 2-group	strict 2-groupoid
strict monoidal category	strict 2-category
monoidal groupoid	(2,1)-category
2-group	2-groupoid/bigroupoid
monoidal category	2-category/bicategory