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On coalgebras over algebras

A. Balan, A. Kurz
2011 Theoretical Computer Science  
If this is the case, then 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.  ... 
doi:10.1016/j.tcs.2011.03.021 fatcat:7k5ih7fj6remln7z4fyln2jn7i

On coalgebras over algebras [article]

Adriana Balan, Alexander Kurz
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 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  ... 
arXiv:1005.0938v1 fatcat:gykr7gpednbdrbhuacdf4onoai

On Coalgebras over Algebras

Adriana Balan, Alexander Kurz
2010 Electronical Notes in Theoretical Computer Science  
Kurz (UL) On coalgebras over algebras CMCS 2010 15 / 31 I . . .  ...  Kurz (UL)On coalgebras over algebras CMCS 2010 15 / 31Remember L is complete ultrametric space.  ... 
doi:10.1016/j.entcs.2010.07.013 fatcat:xes22ykyzbba3oxjo7qd6xc3fu

Modules Over Monads and Their Algebras

Maciej Pirog, Nicolas Wu, Jeremy Gibbons, Marc Herbstritt
2015 Conference on Algebra and Coalgebra in Computer Science  
Modules 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.  ... 
doi:10.4230/lipics.calco.2015.290 dblp:conf/calco/PirogWG15 fatcat:wqg7gw4qvjh63a3yqpwpfr6sjm

On coreflexive coalgebras and comodules over commutative rings

Jawad Y. Abuhlail
2004 Journal of Pure and Applied Algebra  
In this paper we study dual 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  ... 
doi:10.1016/j.jpaa.2004.04.003 fatcat:h4gnikw55rhgbnqxsy6diefhgm

Coalgebraic coalgebras

D. E. Radford
1974 Proceedings of the American Mathematical Society  
We investigate 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.  ... 
doi:10.1090/s0002-9939-1974-0357474-9 fatcat:ufdgl2s2bnexflrf24t3phyidi

Coalgebraic Coalgebras

D. E. Radford
1974 Proceedings of the American Mathematical Society  
We investigate 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.  ... 
doi:10.2307/2040598 fatcat:q7gg72uxx5fkjiyfxuexmazan4

Coalgebraic tensor product and homology operations

Takuji Kashiwabara
2010 Algebraic and Geometric Topology  
In this paper, we show that Hunton-Turner 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  ... 
doi:10.2140/agt.2010.10.1739 fatcat:57hxraz5onbglig4nbgpkxctoy

Homotopy Theories of Algebras over Operads

V. A. Smirnov
2005 Mathematical Notes  
A chain complex X is called an 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.  ... 
doi:10.1007/s11006-005-0122-z fatcat:kfmaslrrfrcuxge576zk75qu7i

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  ... 

Homotopy theories of algebras over operads

V. A. Smirnov
2005 Homology, Homotopy and Applications  
A chain complex X is called an 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.  ... 
doi:10.4310/hha.2005.v7.n2.a10 fatcat:3s4rktzhhraadgbw7som432hje

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.  ... 

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.  ... 

Quantum homogeneous spaces and coalgebra bundles

Tomasz Brzeziński
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 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 .  ... 
doi:10.1016/s0034-4877(97)85914-9 fatcat:snbjuinvdvdfdb55om2mrsl3tq

An intertwining of a hereditary algebra and a cohereditary coalgebra

Hanni Garminia, Pudji Astuti, Irawati Irawati
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.  ... 
doi:10.11113/mjfas.v4n1.35 fatcat:gwx6qoy7n5c3lm2lyj3r2r5zxm
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