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Monadic NM-algebras
[article]
2017
arXiv
pre-print
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Also, we obtain some conditions under which monadic NM-algebras become monadic Boolean algebras. ...
Finally, we present monadic NM-logic and prove the (chain) completeness of monadic NM-logic based on monadic NM-algebras. ...
Monadic NM-algebras In this section, we introduce and investigate monadic NM-algebras. Then, we prove that monadic NM-algebras faithfully the axioms on quantifiers in monadic predicate NM logic. ...
arXiv:1709.04832v1
fatcat:5a7z5knijvelnhvubi6345btx4
Page 267 of American Mathematical Society. Proceedings of the American Mathematical Society Vol. 9, Issue 2
[page]
1958
American Mathematical Society. Proceedings of the American Mathematical Society
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The monadic algebra A above is free on the r generators {pi,- ++, Pe}. A has nm atoms, and so has Qum — a2"2?—; elements.
We mention, without proof, a few of the properties of this algebra, A. ...
1958] FINITE MONADIC ALGEBRAS 267
hence 3S, =NB(S,) Cie
We now gather our results. By Theorem 1, Lemma 5, and Lemma 4, {p:1,---, pe} is a monadic generating set for A. ...
Page 7320 of Mathematical Reviews Vol. , Issue 2003j
[page]
2003
Mathematical Reviews
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See also 20102, 54033, 68148.
06D Distributive lattices
2003j:06010 06D20 03G25 08B25
Bezhanishvili, Guram (1-NMS; Las Cruces, NM);
Harding, John (1-NMS; Las Cruces, NM)
Functional monadic Heyting algebras ...
(English summary)
Algebra Universalis 48 (2002), no. 1, 1-10.
Monadic Heyting algebras were introduced as the algebraic coun- terparts of the one-variable fragment of intuitionistic logic. ...
Finite Monadic Algebras
1958
Proceedings of the American Mathematical Society
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The monadic algebra A above is free on the r generators {pi, ■ ■ • , pr}. A has nm atoms, and so has r C2r-1}
2»m _ 212 2
1
elements. ...
A monadic algebra A is said to be free on the set of generators GCA if (i) G generates A, and (ii) any map /o of G into a monadic algebra B can be extended to a monadic homomorphism f:A->B. ...
(3.2) We observe, before proceeding, that the algebra A has evidently nm atoms, (one element subsets of S). ...
doi:10.2307/2033149
fatcat:phhisz7xo5clhoj3ytp26lp7ym
Finite monadic algebras
1958
Proceedings of the American Mathematical Society
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The file type is application/pdf.
The monadic algebra A above is free on the r generators {pi, ■ ■ • , pr}. A has nm atoms, and so has r C2r-1}
2»m _ 212 2
1
elements. ...
A monadic algebra A is said to be free on the set of generators GCA if (i) G generates A, and (ii) any map /o of G into a monadic algebra B can be extended to a monadic homomorphism f:A->B. ...
(3.2) We observe, before proceeding, that the algebra A has evidently nm atoms, (one element subsets of S). ...
doi:10.1090/s0002-9939-1958-0094308-5
fatcat:xqgw5gb2v5dirbju3ikhvihfkq
Solving Algebraic Equations Using Coalgebra
2003
RAIRO - Theoretical Informatics and Applications
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This paper presents a categorical approach to algebraic systems of equations which generalizes the traditional approach in two ways i) we define algebraic equations for locally finitely presentable categories ...
Algebraic systems of equations define functions using recursion where parameter passing is permitted. ...
Once this is understood, this would be a very exciting application. φ m (x 1 , . . . , x nm ) = t m (x 1 , . . . , x nm )
Lemma 3. 1 . 1 Let (T, η, µ) be a monad on C and F an endofunctor on C. ...
doi:10.1051/ita:2003021
fatcat:ksands7b4jfibpswdf2pomytg4
Functional distribution monads in functional-analytic contexts
[article]
2017
arXiv
pre-print
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By employing the notion of commutant for enriched algebraic theories and monads, we define the functional distribution monad associated to a given functional-analytic context. ...
The construction takes place within a categorical setting for generalized functional analysis, called a functional-analytic context, formulated in terms of a given monad or algebraic theory T enriched ...
For all n, m ∈ N, let us denote by ι nm : T aff (n, m) → T (n, m) the equalizer of the morphisms φ nm = T (δ n , m) : T (n, m) → T (1, m) and ψ nm = Proposition 8.2. ...
arXiv:1701.08152v3
fatcat:tn3wd45hwveilgtwfkzaiqlwzi
Relating computational effects by ⊤⊤-lifting
2013
Information and Computation
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We consider the problem of establishing a relationship between two interpretations of base type terms of a λ c -calculus extended with algebraic operations. ...
the global counter monad. ...
It has the inverse Gef T : Alg(T , D, C) → C(C, T D) given by Gef T (α) = nm −1 C,T D (α D • nm D,T D (η D )). Let T ′ = (T ′ , η ′ , µ ′ , θ ′ ) be another strong monad on C. ...
doi:10.1016/j.ic.2012.10.014
fatcat:3dfxgbt5k5eo5o6ovrzvip7vae
Relating Computational Effects by ⊤ ⊤-Lifting
[chapter]
2011
Lecture Notes in Computer Science
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We consider the problem of establishing a relationship between two interpretations of base type terms of a λ c -calculus extended with algebraic operations. ...
the global counter monad. ...
It has the inverse Gef T : Alg(T , D, C) → C(C, T D) given by Gef T (α) = nm −1 C,T D (α D • nm D,T D (η D )). Let T ′ = (T ′ , η ′ , µ ′ , θ ′ ) be another strong monad on C. ...
doi:10.1007/978-3-642-22012-8_13
fatcat:of4pmpczifdhjk6thzwgjwnj3u
Page 550 of Mathematical Reviews Vol. 51, Issue 2
[page]
1976
Mathematical Reviews
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In the case of the monadic category Vect, the Eilenberg-Moore algebra structure is explored in detail to show how it yields the usual algebra structure of a vector space. ...
Linton’s (unpublished) resuit that Ban is equivalent to the Eilenberg-Moore category of algebras of the monad is given. ...
Lawvere theories, finitary monads and Cauchy-completion
2014
Journal of Pure and Applied Algebra
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We also account for other phenomena from the enriched viewpoint: the equivalence of the algebras for a finitary monad with the models of the corresponding Lawvere theory; the functorial semantics in arbitrary ...
categories with finite powers; and the existence of left adjoints to algebraic functors. ...
The tensor of X (n) by y m is X (nm) , as witnessed by the element i = (π 1 , . . . , π nm ) ∈ LM m (X (n) , X (nm) ) = M nm (X, X) nm . ...
doi:10.1016/j.jpaa.2014.02.018
fatcat:fr5zkiw5rrg4rockmrwevdcm6a
Graded Algebraic Theories
[article]
2020
arXiv
pre-print
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We provide graded extensions of algebraic theories and Lawvere theories that correspond to graded monads. ...
We prove that graded algebraic theories, graded Lawvere theories, and finitary graded monads are equivalent via equivalence of categories, which extends the equivalence for monads. ...
The inverse of the unit η T is the family of identity functions 1 : F T nm → F T nm. ...
arXiv:2002.06784v2
fatcat:qzvoodkv4vdl3cajfaws766qk4
Lawvere theories, finitary monads and Cauchy-completion
[article]
2013
arXiv
pre-print
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We also account for other phenomena from the enriched viewpoint: the equivalence of the algebras for a finitary monad with the models of the corresponding Lawvere theory; the functorial semantics in arbitrary ...
categories with finite powers; and the existence of left adjoints to algebraic functors. ...
The tensor of X (n) by y m is X (nm) , as witnessed by the element i = (π 1 , . . . , π nm ) ∈ LM m (X (n) , X (nm) ) = M nm (X, X) nm . ...
arXiv:1307.2963v1
fatcat:peplpb2azbhmdcb7dxqkmavaa4
Graded Algebraic Theories
[chapter]
2020
Lecture Notes in Computer Science
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We provide graded extensions of algebraic theories and Lawvere theories that correspond to graded monads. ...
We prove that graded algebraic theories, graded Lawvere theories, and finitary graded monads are equivalent via equivalence of categories, which extends the equivalence for monads. ...
Monads correspond to algebraic theories [5] . ...
doi:10.1007/978-3-030-45231-5_21
fatcat:e26xprsfgvey5ktqn6xduav6em
Page 5415 of Mathematical Reviews Vol. , Issue 96i
[page]
1996
Mathematical Reviews
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Loring (1-NM-S; Albuquerque, NM)
961:46084 46L85 19D55 22D25 46L05 Ji, Ronghui (1-INPI; Indianapolis, IN) Trace invariant and cyclic cohomology of twisted group C*-algebras. (English summary) J. ...
In general uv :=[0] is not a monad and does not induce a vector space topology. ...
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