Categories of modules, comodules and contramodules over representations
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Mamta Balodi
Abstract
We study and relate categories of modules, comodules and contramodules over a representation of a small category taking values in (co)algebras, in a manner similar to modules over a ringed space. As a result, we obtain a categorical framework which incorporates all adjoint functors between these categories in a natural manner. Various classical properties of coalgebras and their morphisms arise naturally within this theory. We also consider cartesian objects in each of these categories, which may be viewed as counterparts of quasi-coherent sheaves over a scheme. We study their categorical properties using cardinality arguments. Our focus is on generators for these categories and on Grothendieck categories, because the latter may be treated as replacements for noncommutative spaces.
Funding source: Science and Engineering Research Board
Award Identifier / Grant number: MTR/2017/000112
Award Identifier / Grant number: PDF/2020/000670
Funding statement: A. Banerjee was partially supported by SERB Matrics fellowship MTR/2017/000112. S. Ray was partially supported by SERB National Postdoctoral Fellowship PDF/2020/000670.
Acknowledgements
The authors are grateful to L. Positselski for a useful discussion.
References
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© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- On Mukhin’s necessary and sufficient condition for the validity of the local limit theorem
- Non-commutative Khinchine-type inequality for dependent random variables and overview of its applications in data science
- Connections and genuinely ramified maps of curves
- Caustics of pseudo-spherical surfaces in the Euclidean 3-space
- On liftings of modular forms and Weil representations
- Approximation via statistical measurable convergence with respect to power series for double sequences
- Global existence, scattering, rigidity and inverse scattering for some quasilinear hyperbolic systems
- Gem-induced trisections of compact PL 4-manifolds
- Categories of modules, comodules and contramodules over representations
- On the Iwasawa invariants of BDP Selmer groups and BDP p-adic L-functions
- On the largest prime factor of non-zero Fourier coefficients of Hecke eigenforms
- Congruence subgroups and crystallographic quotients of small Coxeter groups
- Some Betti numbers of the moduli of 1-dimensional sheaves on ℙ2
- Hardy and BMO spaces on Weyl chambers
- De Branges–Rovnyak spaces and local Dirichlet spaces of higher order
Artikel in diesem Heft
- Frontmatter
- On Mukhin’s necessary and sufficient condition for the validity of the local limit theorem
- Non-commutative Khinchine-type inequality for dependent random variables and overview of its applications in data science
- Connections and genuinely ramified maps of curves
- Caustics of pseudo-spherical surfaces in the Euclidean 3-space
- On liftings of modular forms and Weil representations
- Approximation via statistical measurable convergence with respect to power series for double sequences
- Global existence, scattering, rigidity and inverse scattering for some quasilinear hyperbolic systems
- Gem-induced trisections of compact PL 4-manifolds
- Categories of modules, comodules and contramodules over representations
- On the Iwasawa invariants of BDP Selmer groups and BDP p-adic L-functions
- On the largest prime factor of non-zero Fourier coefficients of Hecke eigenforms
- Congruence subgroups and crystallographic quotients of small Coxeter groups
- Some Betti numbers of the moduli of 1-dimensional sheaves on ℙ2
- Hardy and BMO spaces on Weyl chambers
- De Branges–Rovnyak spaces and local Dirichlet spaces of higher order
