monoidaladj.

Brit.

/mɒˈnɔɪdl/, U.S.

/məˈnɔɪd(ə)l/

Origin: Formed within English, by derivation. Etymons: monoid n., -al suffix¹.

Etymology: < monoid n. + -al suffix¹.

Mathematics.

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).

单词	monoidal
释义	monoidaladj. Brit. /mɒˈnɔɪdl/, U.S. /məˈnɔɪd(ə)l/ Origin: Formed within English, by derivation. Etymons: monoid n., -al suffix¹. Etymology: < monoid n. + -al suffix¹. 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). < adj.1894
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