The 3-by-3 lemma for regular Goursat categories.
The categories of presheaves containing any category of algebras [Book]
The category of compactifications and its coreflections
We define “the category of compactifications”, which is denoted CM, and consider its family of coreflections, denoted corCM. We show that corCM is a complete lattice with bottom the identity and top an interpretation of the Čech–Stone . A corCM implies the assignment to each locally compact, noncompact a compactification minimum for membership in the “object-range” of . We describe the minimum proper compactifications of locally compact, noncompact spaces, show that these generate the atoms...
The category of nonindexed algebras and weak homomorphisms
The category of opetopes and the category of opetopic sets.
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 closure of a model category
The colimits in the generalized algebraic categories
The commuting of coreflectors in uniform spaces with completion
The coproduct of totally convex spaces
The epis of
The epis of the category of ordered algebras and -continuous homomorphisms
The existence and construction of Lax limits
The extensive completion of a distributive category.
The free adjunction
The Geometry of Self-adjunction
The Heyting doctrines
The infinite minimal rich monoid
The internal and external aspect of logic and set theory in elementary topoi
The Krull-Schmidt theorem for categories of finitely generated modules over valuation domains.