monoidaladj.
/mɒˈnɔɪdl/, U.S. /məˈnɔɪd(ə)l/ Mathematics.
1.
a. Of, relating to, or designating a monoid (monoid n. 1); spec. designating a transformation of a space into a monoid. Now rare.
ΘΚΠ
the world > relative properties > number > geometry > geometric space > [adjective] > of topological space
monoidal1894
metrizable1927
complete1934
triangulable1940
monoidal1943
1894 Ann. Math. 8 39 3 monoidal axes lie in each plane in space.
1914 Trans. Amer. Math. Soc. 15 241 The transformation which interchanges these points is a monoidal cubic involution.
1924 Ann. Math. 25 279 A monoidal space transformation is defined as one in which the planes of space are transformed into surfaces (monoids) of order n with a common (n − 1)-fold point.
1952 Proc. Amer. Math. Soc. 3 346 It is a monoidal transformation since the homaloids in [3] are monoids.
b. Designating a transformation of a topological space that is performed in order to remove or circumvent singularities in the space (see quot. 1943).
ΘΚΠ
the world > relative properties > number > geometry > geometric space > [adjective] > of topological space
monoidal1894
metrizable1927
complete1934
triangulable1940
monoidal1943
1943 O. Zariski in Trans. Amer. Math. Soc. 53 535 Let W be the irreducible subvariety of V defined by . The birational transformation T determined by the ideal ..is called a monoidal transformation transformation of center W.
1968 Amer. Jrnl. Math. 90 1 My approach is to use the desingularization of subvarieties by successions of monoidal transformations.
1988 Trans. Amer. Math. Soc. 309 320 The surface V′ is obtained by applying two monoidal transformations.
2. Of, relating to, or involving a monoid or monoids (monoid n. 2).
ΚΠ
1966 S. Eilenberg & G. M. Kelly in Conf. Categorical Algebra 423 Closed categories which possess a tensor product defined by the adjointness relation (A⊗B,C) ≅ (A(BC))..lead us to the notion of a monoidal category.
1970 Trans. Amer. Math. Soc. 147 574 Under these circumstances the homotopy category becomes a monoidal closed category.
1994 Amer. Jrnl. Math. 116 1088 A monoidal space..is a topological space..endowed with a sheaf of monoids.
Derivatives
moˈnoidally adv.
ΚΠ
1973 Amer. Jrnl. Math. 95 298 We shall say a pair (R,S) is monoidally reducible if there exists a monoidal transform R′ of R so that S dominates R′.
2001 N.Y. Jrnl. Math. (Electronic ed.) 7 258 Every monoidal category is monoidally equivalent to a strict monoidal category.
This is a new entry (OED Third Edition, December 2002; most recently modified version published online March 2022).
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adj.1894