Abstract
Projective representations and injective representations are key concepts in representation theory. A representation P is called projective if the functor Hom(P, −) maps surjective morphisms to surjective morphisms. Dually a representation I is called injective if the functor Hom(−, I) maps injective morphisms to injective morphisms.
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References
Maurice Auslander and Idun Reiten, Representation theory of Artin algebras. III. Almost split sequences, Comm. Algebra 3 (1975), 239–294. MR 0379599 (52 #504)
Joseph J Rotman, An introduction to homological algebra, Springer, 2009.
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Schiffler, R. (2014). Projective and Injective Representations. In: Quiver Representations. CMS Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-09204-1_2
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DOI: https://doi.org/10.1007/978-3-319-09204-1_2
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