The 3-by-3 lemma for regular Goursat categories.
The category of uniform spaces as a completion of the category of metric spaces
A criterion for the existence of an initial completion of a concrete category universal w.r.tḟinite products and subobjects is presented. For metric spaces and uniformly continuous maps this completion is the category of uniform spaces.
The Krull-Schmidt theorem for categories of finitely generated modules over valuation domains.
The Linton theorem revisited
The reflectiveness of covering morphisms in algebra and geometry.
The semigroup of Fredholm operators.
The separated extensional Chu category.
The strong amalgamation property and (effective) codescent morphisms.
The tower and regular decomposition
Topologically-algebraic structure functors full reflective or coreflective restrictions of semitopological functors