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On coalgebras over algebras

2011
*
Theoretical Computer Science
*

If this is the case, then

doi:10.1016/j.tcs.2011.03.021
fatcat:7k5ih7fj6remln7z4fyln2jn7i
*one*can recover the initial*algebra*for the lifted endofunctor H as the free M-*algebra*built*on*the initial T -*algebra*. ... completion of the free M-*algebra**on*the initial T -*algebra*. for the lifted functor, with respect to the usual ultrametric inherited from the final sequence. ... The final*coalgebra*{0, 1} A * can be identified with the set of formal languages P (A * )*over*A. ...##
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On coalgebras over algebras
[article]

2010
*
arXiv
*
pre-print

As an application we introduce the notion of commuting pair of endofunctors with respect to the monad M and show that under reasonable assumptions, the final

arXiv:1005.0938v1
fatcat:gykr7gpednbdrbhuacdf4onoai
*coalgebra*of*one*of the endofunctors involved ... We extend Barr's well-known characterization of the final*coalgebra*of a Set-endofunctor as the completion of its initial*algebra*to the Eilenberg-Moore category of*algebras*for a Set-monad M for functors ... In the first part of this paper, we show that Barr's theorem [7] extends from*coalgebras**on*Set to*coalgebras**on*the Eilenberg-Moore category of*algebras*Alg(M) for a monad M*on*Set, dropping the assumption ...##
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On Coalgebras over Algebras

2010
*
Electronical Notes in Theoretical Computer Science
*

Kurz (UL)

doi:10.1016/j.entcs.2010.07.013
fatcat:xes22ykyzbba3oxjo7qd6xc3fu
*On**coalgebras**over**algebras*CMCS 2010 15 / 31 I . . . ... Kurz (UL)*On**coalgebras**over**algebras*CMCS 2010 15 / 31Remember L is complete ultrametric space. ...##
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Modules Over Monads and Their Algebras

2015
*
Conference on Algebra and Coalgebra in Computer Science
*

Modules

doi:10.4230/lipics.calco.2015.290
dblp:conf/calco/PirogWG15
fatcat:wqg7gw4qvjh63a3yqpwpfr6sjm
*over*monads (or: actions of monads*on*endofunctors) are structures in which a monad interacts with an endofunctor, composed either*on*the left or*on*the right. ... Moreover, we discuss a connection between modules and*algebraic*effects: left modules have a similar feeling to Eilenberg-Moore*algebras*, and can be seen as handlers that are natural in the variables, ... , whose grant*on*Unifying Theories of Generic Programming (EP/J010995/1) partially supported this work. ...##
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On coreflexive coalgebras and comodules over commutative rings

2004
*
Journal of Pure and Applied Algebra
*

In this paper we study dual

doi:10.1016/j.jpaa.2004.04.003
fatcat:h4gnikw55rhgbnqxsy6diefhgm
*coalgebras*of*algebras**over*arbitrary (Noetherian) commutative rings. ... Our approach in this note is an*algebraically*topological*one*. ... The following result extends observations in [16] (respectively [4] )*on*coÿnitary*algebras**over*Dedekind domains (respectively Noetherian rings) to the case of coÿnitary ÿlters for*algebras**over*arbitrary ...##
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Coalgebraic coalgebras

1974
*
Proceedings of the American Mathematical Society
*

We investigate

doi:10.1090/s0002-9939-1974-0357474-9
fatcat:ufdgl2s2bnexflrf24t3phyidi
*coalgebras*C*over*a field k such ... Our main result is that if C is a*coalgebra**over*an infinite field k and the Jacobs*on*radical Rad C* is nil, there is an n such that an = 0 all a £ Rad C*. ... In this paper we investigate*coalgebras*C*over*a field k such that the dual*algebra*C* is*algebraic*(i.e. k\_a\ is finite dimensional for all a e C*)" Such*coalgebras*we call*coalgebraic*. ...##
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Coalgebraic Coalgebras

1974
*
Proceedings of the American Mathematical Society
*

We investigate

doi:10.2307/2040598
fatcat:q7gg72uxx5fkjiyfxuexmazan4
*coalgebras*C*over*a field k such ... Our main result is that if C is a*coalgebra**over*an infinite field k and the Jacobs*on*radical Rad C* is nil, there is an n such that an = 0 all a £ Rad C*. ... In this paper we investigate*coalgebras*C*over*a field k such that the dual*algebra*C* is*algebraic*(i.e. k\_a\ is finite dimensional for all a e C*)" Such*coalgebras*we call*coalgebraic*. ...##
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Coalgebraic tensor product and homology operations

2010
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Algebraic and Geometric Topology
*

In this paper, we show that Hunton-Turner

doi:10.2140/agt.2010.10.1739
fatcat:57hxraz5onbglig4nbgpkxctoy
*coalgebraic*tensor product respects various actions of Hopf*algebras*of homology operations. ... Definition 5.1 Let A ; be a*coalgebraic*ring*over*R and ‚ a Hopf*algebra**over*R. ... The purpose of this paper is to answer this question, namely we prove: Theorem 1.1 Let ‚ be a Hopf*algebra**over*the base-ring R, A ; a commutative*coalgebraic*ring*over*R, M ; , N ;*coalgebraic*modules ...##
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Homotopy Theories of Algebras over Operads

2005
*
Mathematical Notes
*

A chain complex X is called an

doi:10.1007/s11006-005-0122-z
fatcat:kfmaslrrfrcuxge576zk75qu7i
*algebra*(*coalgebra*)*over*an operad E or simply E-*algebra*(E-*coalgebra*) if there is given a family of mappings µ(j) : E(j) ⊗ X ⊗j → X, (τ (j) : X → Hom(E(j); X ⊗j ), which ... of 1-connected topological spaces is equivalent to the homotopy theory of 1-connected E ∞ -*coalgebras*(E ∞ -*algebras*). ... Any*algebra*(*coalgebra*)*over*E ∞ -operad is called E ∞ -*algebra*(E ∞ -*coalgebra*). 6. ...##
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Page 8740 of Mathematical Reviews Vol. , Issue 2001M
[page]

2001
*
Mathematical Reviews
*

The first

*one*recalls the notions of G-graded*coalgebra*and*one*-sided G-graded co- module*over*a G-graded*coalgebra*, where G is a group. ... The last section of the paper is devoted to studying the action of G-graded Morita- Takeuchi contexts*on*certain G-graded*coalgebras*; namely those G-graded*coalgebras*A where A, is isomorphic to*one*of ...##
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Homotopy theories of algebras over operads

2005
*
Homology, Homotopy and Applications
*

A chain complex X is called an

doi:10.4310/hha.2005.v7.n2.a10
fatcat:3s4rktzhhraadgbw7som432hje
*algebra*(*coalgebra*)*over*an operad E or simply E-*algebra*(E-*coalgebra*) if there is given a family of mappings µ(j) : E(j) ⊗ X ⊗j → X, (τ (j) : X → Hom(E(j); X ⊗j ), which ... of 1-connected topological spaces is equivalent to the homotopy theory of 1-connected E ∞ -*coalgebras*(E ∞ -*algebras*). ... Any*algebra*(*coalgebra*)*over*E ∞ -operad is called E ∞ -*algebra*(E ∞ -*coalgebra*). 6. ...##
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Page 4147 of Mathematical Reviews Vol. , Issue 97G
[page]

1997
*
Mathematical Reviews
*

acting

*on*associative*algebras*. ...*over*B with bimod- ule 9V8 = B@, V @4B and (#*)* is a*coalgebra**over*eBe with bimodule e8V%e. ...##
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Page 8 of Mathematical Reviews Vol. , Issue 98E
[page]

1998
*
Mathematical Reviews
*

Let A be a

*coalgebra**over*a field of characteristic #2 with a comultiplication A. Then A is a Jordan*coalgebra*if its dual*algebra*A* isa Jordan*algebra*. ... Russian summary )*Algebra*i Logika 35 (1996), no. 5, 529-542, 624; translation in*Algebra*and Logic 35 (1996), no. 5, 296-304. Consider a*coalgebra*A*over*a field of characteristic 42,3, and 5. ...##
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Quantum homogeneous spaces and coalgebra bundles

1997
*
Reports on mathematical physics
*

It is shown that quantum homogeneous spaces of a quantum group H can be viewed as fibres of quantum fibrations with the total space H that are dual to

doi:10.1016/s0034-4877(97)85914-9
fatcat:snbjuinvdvdfdb55om2mrsl3tq
*coalgebra*bundles. ... By an*algebra*we mean an associative*algebra**over*k with unit denoted by 1. In a*coalgebra*C, ∆ is the coproduct and ǫ : C → k is the counit. ... In other words we have a*coalgebra*and a dual*coalgebra*principal bundles, E q (2)(X q , C, c 0 )*over*X q with fibre C and E q (2)(C, X q , κ)*over*C with fibre X q . ...##
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An intertwining of a hereditary algebra and a cohereditary coalgebra

2008
*
Malaysian Journal of Fundamental and Applied Sciences
*

*On*the other hand if C is a finitely dimensional cohereditary F -

*coalgebra*then thedual ( ) F C∗ =Hom C,F is a hereditary F -

*algebra*. ... Particularly we show that properties similar to the above results areobtained for a class of

*algebras*and

*coalgebras*

*over*a self injective commutative ring R where the

*algebras*andcoalgebras, as R -modules ...

*On*the other hand if C is a finitely dimensional cohereditary F -

*coalgebra*then its dual ( ) F C Hom C F * = , is a hereditary F -

*algebra*. ...

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