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Monadic convergence structures revisited
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DOI：10.1016/j.fss.2020.06.007.png)
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Abstract
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For L-power enriched monad (T, tau), the notions of pretopological and topological T -convergence structures are introduced from the viewpoint of topology. It is shown that the pretopological T -convergence structures are exactly the reflexive and unitary (T, L)-relations and the topological pretopological T -convergence structures are precisely (T, L)-algebras. When (T, tau) is the stratified L-filter monad, the L-ordered filter monad, or the L-concave filter monad, the general setting produces known results on stratified L-convergence structures, L-ordered convergence structures and L-concave structures. (C) 2020 Elsevier B.V. All rights reserved.
Keywords:
L-power enriched monad
Lax algebra
Convergence structure
Concave structure
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