nLab flexible magmoid

Contents

Context

Category theory

Algebra

Categorification

Contents

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 QQ such that for every two objects a,bOb(Q)a,b \in Ob(Q) and for every two morphisms f:abf:a \to b and g:bag:b \to a,

f(gf)=(fg)f. f \circ (g \circ f) = (f \circ g) \circ f \,.

Examples

algebraic structureoidification
magmamagmoid
pointed magma with an endofunctionsetoid/Bishop set
unital magmaunital magmoid
quasigroupquasigroupoid
looploopoid
semigroupsemicategory
monoidcategory
anti-involutive monoiddagger category
associative quasigroupassociative quasigroupoid
groupgroupoid
flexible magmaflexible magmoid
alternative magmaalternative magmoid
absorption monoidabsorption category
cancellative monoidcancellative category
rigCMon-enriched category
nonunital ringAb-enriched semicategory
nonassociative ringAb-enriched unital magmoid
ringringoid
nonassociative algebralinear magmoid
nonassociative unital algebraunital linear magmoid
nonunital algebralinear semicategory
associative unital algebralinear category
C-star algebraC-star category
differential algebradifferential algebroid
flexible algebraflexible linear magmoid
alternative algebraalternative linear magmoid
Lie algebraLie algebroid
monoidal poset2-poset
strict monoidal groupoid?strict (2,1)-category
strict 2-groupstrict 2-groupoid
strict monoidal categorystrict 2-category
monoidal groupoid(2,1)-category
2-group2-groupoid/bigroupoid
monoidal category2-category/bicategory

Last revised on May 23, 2021 at 15:04:52. See the history of this page for a list of all contributions to it.