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In mathematics, a comodule or corepresentation is a concept dual to a module. The definition of a comodule over a coalgebra is formed by dualizing the
Comodule
on the site, giving a topos-theoretic notion of modules. Duallypg 2, comodules over a Hopf algebroid are the purely algebraic analogue of this construction
Comodule over a Hopf algebroid
Comodule_over_a_Hopf_algebroid
Type of vehicle
capabilities at APG". The United States Army Homepage. "Blog — COMODULE". www.comodule.com. Archived from the original on March 4, 2016. Retrieved Feb
Unmanned_ground_vehicle
Study of Hopf algebras via their actions on vector spaces and associative algebras
coreprepresentation or comodule of a coalgebra. Since Hopf algebras are bialgebras, they can have both modules and comodules, and as for modules, trivial comodules and tensor
Representation theory of Hopf algebras
Representation_theory_of_Hopf_algebras
the Pareigis Hopf algebra is the Hopf algebra over a field k whose left comodules are essentially the same as complexes over k, in the sense that the corresponding
Pareigis_Hopf_algebra
Algebraic structure decomposed into a direct sum
corresponding Hilbert–Poincaré series. Graded (mathematics) Graded algebra Comodule Graded module Littlewood–Richardson rule Bourbaki, N. (1974) Algebra I
Graded_vector_space
Concept in Hopf algebra and weak Hopf algebra
a left H-comodule algebra, and C a right H-module coalgebra. A left-right Doi-Hopf (H,A,C)-module M is a left A-module and a right C-comodule via β:M→M⊗C
Doi-Hopf_module
Category with direct sums and certain types of kernels and cokernels
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
Abelian_category
language of comodules, they endow S ∗ ( E ) {\displaystyle S_{\ast }(E)} and S ∗ ( X ) {\displaystyle S_{\ast }(X)} with differential graded comodule structures
Eilenberg–Moore spectral sequence
Eilenberg–Moore_spectral_sequence
Structure dual to a unital associative algebra
to the concept of representation for algebras is a corepresentation or comodule. Cofree coalgebra Measuring coalgebra Dialgebra Yokonuma (1992). "Prop
Coalgebra
action of H on V, ( V , δ ) {\displaystyle (V,\delta \;)} is a left H-comodule, where δ : V → H ⊗ V {\displaystyle \delta :V\to H\otimes V} denotes the
Yetter–Drinfeld_category
as a natural B-module. Tomasz Brzezinski; Robert Wisbauer, Corings and Comodules. London Math. Soc. Lect. Note Ser., 309. Cambridge University Press, 2003
Depth of noncommutative subrings
Depth_of_noncommutative_subrings
American mathematician
Kathryn; Shipley, Brooke (2016). "Waldhausen K-theory of spaces via comodules". Advances in Mathematics. 290: 1079–1137. arXiv:1402.4719. doi:10.1016/j
Kathryn_Hess
Construct in mathematics
above always has objects. Note this can be applied to the situation of comodules over Hopf-algebroids to construct algebraic models of gerbes over affine
Gerbe
Algebraic construct of interest in theoretical physics
class of pointed Hopf algebras, meaning that all simple left or right comodules are 1-dimensional and thus the sum of all its simple subcoalgebras forms
Quantum_group
H𝔽p∗(H𝔽p)=𝒜∗ is the dual Steenrod algebra. Since E∗(X) is an E∗(E)-comodule, we can form the bigraded group ExtE∗(E)(E∗(𝕊),E∗(X)) which contains the
Adams_resolution
Various mathematical dualites
Leonid: arXiv:0905.2621 Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence., Mem. Amer. Math. Soc. 212 (2011), no. 996
Koszul_duality
ground field; in this case, the Hopf algebroid (H, R) is a Hopf algebra. Comodule over a Hopf algebroid Ravenel, Douglas C. (1986). Complex cobordism and
Hopf_algebroid
Exact homotopy case
G ) {\displaystyle K_{0}(BG)} as a K 0 ( K ) {\displaystyle K_{0}(K)} -comodule for any compact, connected Lie group. L. Schwartz (1983), "K-théorie et
Classifying_space_for_U(n)
Algebraic structure used in theoretical physics
Likewise the representations of this Hopf algebra turn out to be Z2-graded comodules. This Hopf algebra gives the global properties of the supergroup. There
Supergroup_(physics)
Technique from algebraic geometry
F ) {\displaystyle a:F\to T(F)} (despite the name, they are more like comodules than coalgebras). Then the key point here is that a T {\displaystyle T}
Faithfully_flat_descent
Theorem relating to algebraic topology
on 2004-12-07 Landweber, Peter S. (1976). "Homological properties of comodules over M U ∗ ( M U ) {\displaystyle MU_{*}(MU)} and B P ∗ ( B P ) {\displaystyle
Landweber exact functor theorem
Landweber_exact_functor_theorem
American mathematician (born 1940)
Izvestija, issue 1, 1967, pg.827 Landweber Homological properties of comodules over MU*(MU) and BP*(BP), American Journal of Mathematics, issue 98, 1976
Peter_Landweber
Concept in category theory
S2CID 189829500. Brzezinski, Tomasz; Wisbauer, Robert (2003). Corings and Comodules. London Mathematical Society Lecture Note Series. Vol. 309. Cambridge
Distributive law between monads
Distributive_law_between_monads
Concept in mathematical category theory
Ivan; Smith, Patrick F. (eds.). Notes on formal smoothness. Modules and Comodules. arXiv:0710.5527. doi:10.1007/978-3-7643-8742-6. Lawvere, F. William (2007)
Q-category
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