Construct · 2 fields · 4 citations
One name. Different field. Different construct. One map.
● jingle · one word, two constructs Nearest construct by meaningharmonycompare the meaningsEvery construct on the map is compared with every other by the meaning of its definitions, and the closest one is surfaced here. The nearest construct to monad is harmony.
Hold this as a prompt, not a verdict. Two constructs sitting close in meaning is a reason to read them side by side and decide for yourself whether they are one idea under two names. It is not proof that they are. Compare the meanings in the Collider.
Spokes are fields; dashed arcs are shared lineage. Tap a field for its definition, unit, and measures.
Drag to watch the word get claimed. Each field appears at the publication date of the earliest source cited for it. Tap a year to see which.
In Leibniz's 1714 Monadology, a monad is a simple, indivisible, immaterial substance without parts, the ultimate unit from which all composite things are built. Each monad is said to be windowless, meaning it does not causally interact with others, and it mirrors the whole universe from its own point of view while its inner states unfold according to a pre-established harmony. The Greek word (from monas, a unit) had appeared earlier in Pythagorean and Renaissance thought, but Leibniz fixed this metaphysical meaning of a soul-like elementary substance. This referent is a philosophical unit of being, not an abstract object in a category of functors or a single-celled organism under a microscope.[1]
Roger Godement introduced the underlying construction in his 1958 Topologie algébrique et théorie des faisceaux, where he called it the standard construction built from a pair of adjoint functors. Saunders Mac Lane's 1971 Categories for the Working Mathematician established the now-standard name monad: an endofunctor on a category together with two natural transformations, a unit and a multiplication, that satisfy associativity and identity laws, often summarised as a monoid in the category of endofunctors. Eugenio Moggi's 1991 work carried the same construct into computer science, using monads to structure notions of computation such as state, exceptions, and input and output, which is the meaning familiar in functional programming. This referent is a formal algebraic structure on maps between mathematical objects, not a soul-like substance or a living cell.[2][3][4]
Next
See how monad sits against neighbouring constructs in the Collider, or export every reference on this page in one click.
Open in ColliderExport BibTeXReport this collisionCited on this page?
If your work is cited behind one of these entries, you know better than we do whether we captured the meaning right. Confirm it, suggest an edit, or dispute it, and your name goes on the entry as an author who has checked it, linked to your ORCID.
Claim your construct