Abstract and concrete categories
Abstract and concrete categories
Pretopological and topological lattice-valued convergence spaces
Fuzzy Sets and Systems
On many-valued stratified L-fuzzy convergence spaces
Fuzzy Sets and Systems
A common framework for lattice-valued uniform spaces and probabilistic uniform limit spaces
Fuzzy Sets and Systems
Subcategories of lattice-valued convergence spaces
Fuzzy Sets and Systems
Stratified L-ordered convergence structures
Fuzzy Sets and Systems
Gähler's neighborhood condition for lattice-valued convergence spaces
Fuzzy Sets and Systems
On stratified L-convergence spaces: Pretopological axioms and diagonal axioms
Fuzzy Sets and Systems
Diagonal conditions for lattice-valued uniform convergence spaces
Fuzzy Sets and Systems
Modifications: Lattice-valued structures
Fuzzy Sets and Systems
p-Topologicalness and p-regularity for lattice-valued convergence spaces
Fuzzy Sets and Systems
Enriched lattice-valued convergence groups
Fuzzy Sets and Systems
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We define a category of stratified L-generalized convergence spaces for the case where the lattice is an enriched cl-premonoid. We then investigate some of its categorical properties and those of its subcategories, in particular the stratified L-principal convergence spaces and the stratified L-topological convergence spaces. For some results we need to introduce a new condition on the lattice (which is always true in the case where the lattice is a frame, but not always true in the more general case). As examples where we may apply the more general lattice context we examine the stratified L-topological spaces and probabilistic limit spaces. We show that the category of stratified L-topological spaces is a reflective subcategory of our category and that the category of probabilistic limit spaces under a T-norm is both a reflective and a coreflective subcategory of our category if we choose the lattice context appropriately.