A Cartesian monoid is a monoid, with additional structure of pairing and projection operators. It was first formulated by Dana Scott and Joachim Lambek independently.[1]
^Statman, Rick (1997), "On Cartesian monoids", Computer science logic (Utrecht, 1996), Lecture Notes in Computer Science, vol. 1258, Berlin: Springer, pp. 446–459, doi:10.1007/3-540-63172-0_55, MR 1611514.
A Cartesianmonoid is a monoid, with additional structure of pairing and projection operators. It was first formulated by Dana Scott and Joachim Lambek...
is a free monoid. Transition monoids and syntactic monoids are used in describing finite-state machines. Trace monoids and history monoids provide a foundation...
algebraic structure is a monoid, usually called the full linear monoid, but occasionally also full linear semigroup, general linear monoid etc. It is actually...
ISBN 0-444-87508-5. "Ct.category theory - is the category commutative monoidscartesian closed?". Backus, John (1981). Function level programs as mathematical...
more formal language, P ( A ) {\displaystyle P(A)} is the Cartesian product of the free monoids of the Σ k {\displaystyle \Sigma _{k}} . The superscript...
separate sorting algorithm. The monoid of words over an alphabet A is the free monoid over A. That is, the elements of the monoid are the finite sequences (words)...
theory; among its many advantages, the category of equilogical spaces is a cartesian closed category, whereas the category of domains is not. In 1994, he was...
precisely the monoid objects in the cartesian monoidal category Set. Further, any (small) strict monoidal category can be seen as a monoid object in the...
Michael (2013), In Praise of Quaternions (PDF), McGill University Cartesianmonoid Michael K. Brame "The recipients of the Jeffery-Williams Prize". Canadian...
forms a free monoid under the operation of concatenation of sequences, with sequence reversal as an involution. A rectangular band on a Cartesian product of...
abelian. Archimedean groups can be generalised to Archimedean monoids, linearly ordered monoids that obey the Archimedean property. Examples include the natural...
{\displaystyle E} -categories is called a cartesian functor if it takes cartesian morphisms to cartesian morphisms. Cartesian functors between two E {\displaystyle...
topological notions. Varieties of finite monoids, varieties of finite ordered semigroups and varieties of finite ordered monoids are defined similarly. This notion...
arises as the function composition of endomorphisms over any commutative monoid. The theory of (associative) algebras over commutative rings can be generalized...
letters. A system of equations is a subset E of the Cartesian product X∗ × X∗ of the free monoid (finite strings) over X with itself. The system E is...
M. To construct the Grothendieck group K of a commutative monoid M, one forms the Cartesian product M × M {\displaystyle M\times M} . The two coordinates...
and codomain are the same set X is a left zero of the full transformation monoid on X, which implies that it is also idempotent. It has zero slope or gradient...
the case. For example, a monoid may be viewed as a category with a single object, whose morphisms are the elements of the monoid. The second fundamental...
the monoidal identity object I of M, being an identity for ⊗ only in the monoid-theoretic sense, and even then only up to canonical isomorphism (λ, ρ)....
extension of a posetal category to a 2-category having the same 1-cells are monoids. Some lattice-theoretic structures are definable as posetal categories...
cases in depth. Suppose V and W are vector spaces over the field K. The cartesian product V × W can be given the structure of a vector space over K (Halmos...
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