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2023•arXiv (Cornell University)Open access

Heavily separable functors of the second kind and applications

Abhishek Banerjee, Subhajit Das

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Abstract

We introduce heavily separable functors of the second kind and study them in three different situations. The first of these is with restrictions and extensions of scalars for modules over small preadditive categories. The second is with free functors taking values in Eilenberg-Moore categories associated to a monad or a comonad. Finally, we consider entwined modules and give if and only if conditions for heavy separability of the second kind for functors forgetting either the comodule action or the module action.

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We introduce heavily separable functors of the second kind and study them in three different situations. The first of these is with restrictions and extensions of scalars for modules over small preadditive categories. The second is with free functors taking values in Eilenberg-Moore categories associated to a monad or a comonad. Finally, we consider entwined modules and give if and only if conditions for heavy separability of the second kind for functors forgetting either the comodule action or the module action.

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Available abstract

We introduce heavily separable functors of the second kind and study them in three different situations. The first of these is with restrictions and extensions of scalars for modules over small preadditive categories. The second is with free functors taking values in Eilenberg-Moore categories associated to a monad or a comonad. Finally, we consider entwined modules and give if and only if conditions for heavy separability of the second kind for functors forgetting either the comodule action or the module action.

Key concepts: Monad (category theory), Functor, Action (physics), Separable space, Mathematics, Pure mathematics, Adjoint functors, Algebra over a field

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