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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Bifunctors and adjoint pairs

Authors: J. Fisher Palmquist and David C. Newell
Journal: Trans. Amer. Math. Soc. 155 (1971), 293-303
MSC: Primary 18.10
MathSciNet review: 0274553
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Abstract: We use a definition of tensor products of functors to generalize some theorems of homological algebra. We show that adjoint pairs of functors between additive functor categories correspond to bifunctors and that composition of such adjoint pairs corresponds to the tensor product of the bifunctors. We also generalize some homological characterizations of finitely generated projective modules to characterizations of small projectives in a functor category. We apply our results to adjoint pairs arising from satellites and from a functor on the domain categories.

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Keywords: Functor categories, tensor product of functors, bifunctors, adjoint pairs on functor categories, satellites, duality on functors, small projective functors, adjoints of induced functors
Article copyright: © Copyright 1971 American Mathematical Society