On Actions and Strict Actions in Homological Categories

  title={On Actions and Strict Actions in Homological Categories},
  author={Manfred Hartl and BRUNO LOISEAU},
Let G be an object of a finitely cocomplete homological category C. We study actions of G on objects A of C (defined by Bourn and Janelidze as being algebras over a certain monad TG), with two objectives: investigating to which extent actions can be described in terms of smaller data, called action cores; and to single out those abstract action cores which extend to actions corresponding to semi-direct products of A and G (in a non-exact setting, not every action does). This amounts to… CONTINUE READING
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