The category of nonindexed algebras and weak homomorphisms
The closure of a model category
The epis of
The epis of the category of ordered algebras and -continuous homomorphisms
The -perfect morphisms.
Topologically-algebraic structure functors full reflective or coreflective restrictions of semitopological functors
Totality of colimit closures
Adámek, Herrlich, and Reiterman showed that a cocomplete category is cocomplete if there exists a small (full) subcategory such that every -object is a colimit of -objects. The authors of the present paper strengthened the result to totality in the sense of Street and Walters. Here we weaken the hypothesis, assuming only that the colimit closure is attained by transfinite iteration of the colimit closure process up to a fixed ordinal. This requires some investigations on generalized notions...