Keyboard graph navigation: press N for concepts or E for relations; use arrow keys, Home, and End to move; Enter selects; Shift plus Enter selects and centers; plus and minus zoom; zero fits; Escape clears the selection. Use the visible viewport buttons as alternatives to dragging, wheel, and pinch gestures.
Canonical static concept record
Open this concept in the interactive graphRead the Markdown equivalent
A semigroup with an identity element.
The identity, if it exists in a semigroup, is unique; monoidhood is therefore an existence property rather than freely chosen additional data.
wp-monoidnlab-monoidstacks-algebra-textEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Select semigroups in which a two-sided identity exists; it is then unique.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-monoidstacks-algebra-textEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Require .
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-comm-monoidstacks-algebra-textThis is an authored directed relation from the source endpoint to the target endpoint.
Require every element to have a two-sided inverse.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-groupnlab-groupstacks-algebra-textThis is an authored directed relation from the source endpoint to the target endpoint.
Supply the Monoid structure as one jointly required input.
Feed several structures into a construction junction and impose compatibility between them.
wp-residuated-latticegierz-orderThis is an authored directed relation from the source endpoint to the target endpoint.
Supply the multiplicative monoid.
Feed several structures into a construction junction and impose compatibility between them.
wp-semiringstacks-algebra-textThis is an authored directed relation from the source endpoint to the target endpoint.
Supply the Monoid structure as one jointly required input.
Feed several structures into a construction junction and impose compatibility between them.
wp-topological-semigroupnlab-topological-monoidtopology-without-tearsThis is an authored directed relation from the source endpoint to the target endpoint.
A monoid is precisely a category with one object: monoid elements are endomorphisms and multiplication is composition.
Reinterpret an object, pass to an equivalent presentation, or relate canonically corresponding structures; the carrier may change.
wp-monoidwp-categorynlab-categoryriehl-category-context