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	Comodule -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-09)
		In (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics, a comodule is a concept (additional info and facts about dual) dual to a (A self-contained component (unit or item) that is used in combination with other components) module.
		The definition of a comodule over a (additional info and facts about coalgebra) coalgebra is formed by dualizing the definition of a module over an (additional info and facts about associative algebra) associative algebra.
		Let K be a (A piece of land cleared of trees and usually enclosed) field, and C be a (additional info and facts about coalgebra) coalgebra over K.
	www.absoluteastronomy.com /encyclopedia/c/co/comodule.htm (276 words)

	[No title]
		This is called the extended comodule on M; in case M is itself a free A-module on the set S, then M is called the cofree comodul* *e on M.
		Howeve* r, there is a symmetric monoidal trivial comodule* functor from the category of abe* lian groups to -comodules that takes the abelian group M to A Z M with the trivial comodule* structure given by jL Z 1.
		Suppose (A,) is an amenable Hopf algebroid, and M is a - comodule.
	hopf.math.purdue.edu /Hovey/comodule.txt (11965 words)

	Atlas: Local Theory of Almost Split Sequences for Comodules by William Chin (Site not responding. Last check: 2007-10-09)
		We show that almost split sequences of comodules with a (quasifinitely copresented non-injective) finite dimensional comodule on the right are direct limits of almost split sequences of finite dimensional comodules.
		Starting with a finite dimensional comodule M on the right, we construct these sequences (ending at M) in the category of quasifinite comodules as the direct limit of almost split sequences over finite dimensional subcoalgebras.
		Starting with a finite dimensional comodule on the left, we construct sequences in the dual category to the category of quasifinite comodules as the inverse limit of almost split sequences over finite dimensional subcoalgebras.
	atlas-conferences.com /cgi-bin/abstract/caju-71 (263 words)

	Abelian category -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-09)
		For example, the (additional info and facts about poset) poset of subobjects of any given object A is a (additional info and facts about bounded lattice) bounded lattice.
		The abelian category is also a (additional info and facts about comodule) comodule; Hom(G,A) can be interpreted as an object of A.
		If A is (additional info and facts about complete) complete, then we can remove the requirement that G be finitely generated; most generally, we can form finitary (additional info and facts about enriched limit) enriched limits in A.
	www.absoluteastronomy.com /encyclopedia/a/ab/abelian_category.htm (1377 words)

	Abstract from NYJM - 6-15 - Peter Schauenburg (Site not responding. Last check: 2007-10-09)
		A Hopf module is an $A$-module for an algebra $A$ as well as a $C$-comodule for a coalgebra $C$, satisfying a suitable compatibility condition between the module and comodule structures.
		Many subsequent variants of this were unified independently by Doi and Koppinen; in their version an auxiliary bialgebra $H$, over which $A$ is a comodule algebra and $C$ a module coalgebra, governs the compatibility.
		Another very general type of interaction between $A$ and $C$ is an entwining map as studied by Brzezi\'nski --- without an auxiliary bialgebra.
	www.ii.uj.edu.pl /EMIS/journals/NYJM/j/2000/6-15nf.htm (192 words)

	Comodule - Encyclopedia Glossary Meaning Explanation Comodule (Site not responding. Last check: 2007-10-09)
		Here you will find more informations about Comodule.
		* A coalgebra is a comodule over itself.
		* If M is a module over a K-algebra A, then the set of linear functions from A to K forms a coalgebra, and the set of linear functions from M to K forms a comodule over that coalgebra.
	www.encyclopedia-glossary.com /en/Comodule.html (203 words)

	Abelian category (Site not responding. Last check: 2007-10-09)
		Every abelian category A is a module over the monoidal category of finitely generated abelian groups; that is, we can form a tensor product of a finitely generated abelian group G and any object A of A.
		The abelian category is also a comodule; Hom(G,A) can be interpreted as an object of A.
		If A is complete, then we can remove the requirement that G be finitely generated; most generally, we can form finitary enriched limits in A.
	www.brainyencyclopedia.com /encyclopedia/a/ab/abelian_category.html (995 words)

	Proof of proposition 7.3 (Site not responding. Last check: 2007-10-09)
		-algebra is a comodule algebra for the bialgebra
		-comodule such that multiplication is a morphism of comodules.
		the exterior algebra is a comodule algebra for the latter one, as well.
	www.mathematik.uni-stuttgart.de /mathB/abt/oehms/frt/node8.html (536 words)

	Atlas: Tame/wild dihotomy for coalgebras, quadratic forms and comodules via nilpotent representations of quivers by ...
		We introduce the concepts of tame comodule type and of wild comodule type of a coalgebra C. We prove a week version of Drozd tame/wild dichotomy theorem for coalgebras and a complete version of it for a wide class of coalgebras.
		We shall indicate a role of path colgebras of bound quivers and almost split sequences in the study of coalgebras and comodules.
		We also study comodule theoretical properties of K-coalgebras C by means of the shape of the left Gabriel quiver
	atlas-conferences.com /c/a/q/l/48.htm (405 words)

	[No title]
		The E_{2}-term of this spectral sequence consists of the right derived functors of product in the category of E_{*}E-comodules, and the spectral sequence always converges (with a horizontal vanishing line at E_{infty}) when E is the Johnson-Wilson theory E(n) and each factor of the product is L_{n}-local.
		This spectral sequence is relevant to the chromatic splitting conjecture.
		Naumann niko.naumann@mathematik.uni-regensburg.de We generalise recent results of M. Hovey and N. Strickland on comodule categories for Landweber exact algebras using the formalism of algebraic stacks.
	www.lehigh.edu /~dmd1/mh110.txt (643 words)

	Ferrara Algebra Workshop (Site not responding. Last check: 2007-10-09)
		It can be viewed both as a dual version and a generalisation of the classical Morita context associated to a module over a ring.
		In particular, we study the Morita context associated to a Frobenius coring with a fixed comodule.
		It turns out that the connecting modules in the context are then precisely the comodule and its right dual; in the case where we take the comodule equal to the basic ring A, we recover our earlier results, that unified morita contexts introduced by Doi and by Cohen, Fischman and Montgomery.
	dm.unife.it /ferrara/talks/01vercruysse.html (142 words)

	ATCAT 1999-2000
		We will also use the new formulations to simplify the concept in case the monads in question are idempotent or `KZ'.
		Margaret Beattie, Twisting of comodule algebras and Hopf Galois objects
		Abstract: For a Hopf algebra H and an H-comodule algebra A, the notion of a twisting of A was defined some years ago by Beattie, Chen and Zhang, following work by Zhang for the case of graded rings.
	www.mscs.dal.ca /~pare/Sem99-00.html (1384 words)

	[No title]
		Moreover, the requirement of such covariance unambiguously fixes the bialgebra structure of $SL_q(2)$.
		Let us see now that, quite analogously, the bialgebra structure of $sl_q(2)$ is unambiguously determined if we require the $q$-oscillator algebra to be its covariant comodule.
		Let us invert the problem and consider the $q$-oscillator-type algebra \begin{equation} AB-q^2BA=1 \label{21} \end{equation} as a would-be covariant comodule under the coaction of some bialgebra.
	thsun1.jinr.ru /~alvladim/pap/czjp96.txt (1142 words)

	AMCA: Local Theory of Almost Split Sequences for Comodules by William Chin (Site not responding. Last check: 2007-10-09)
		AMCA: Local Theory of Almost Split Sequences for Comodules by William Chin
		In this talk, we discuss the relationship between almost split sequences for comodules and almost split sequences over finite dimensional subcoalgebras.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts.
	at.yorku.ca /c/a/j/u/71.htm (261 words)

	Moduli Spaces of Commutative Ring Spectra - Paul, Hopkins (ResearchIndex)
		Abstract: Let E be a homotopy commutative ring spectrum, and suppose the ring of cooperations E#E is flat over E#.
		We wish to address the following question: given a commutative E# -algebra A in E#E-comodules, is there an E# -ring spectrum X with E#X = A as comodule algebras?
		We will formulate this as a moduli problem, and give a way -- suggested by work of Dwyer, Kan, and Stover -- of dissecting the resulting moduli space as a tower with layers governed by appropriate Andre-Quillen cohomology...
	citeseer.ist.psu.edu /goerss03moduli.html (766 words)

	[No title]
		We show that these derived functors are closely related to the local cohomology groups of BP_*-modules studied by Greenlees and May; in fact, they coincide with Cech cohomology with respect to I_{n+1}.
		We also construct a spectral sequence of comodules analogous to the Greenlees-May spectral sequence (of modules) converging to BP_(L_n X) whose E_2-term involves L_n^i(BP_X).
		The proofs require getting a partial understanding of injective objects in the category of BP_*BP-comodules.
	www.lehigh.edu /dmd1/public/www-data/h121.txt (2257 words)

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