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.
The Linton theorem revisited
The maximality of the typed lambda calculus and of cartesian closed categories
The Non-Simplicity of Certain Categories of Topological Spaces.
The pure-projective ideal of a module category
The -perfect morphisms.
The reflectiveness of covering morphisms in algebra and geometry.
The semigroup of Fredholm operators.
The separated extensional Chu category.
The shape of a category up to directed homotopy.
The strong amalgamation property and (effective) codescent morphisms.
The structure of initial completions
The structure of the tensor product of with a finite functor between -vector spaces
The paper studies the structure of functors in the category of functors from finite dimensional -vector spaces to -vector spaces, where is a finite functor and is the injective functor . A detection theorem is proved for sub-functors of such functors, which is the basis of the proof that the functors are artinian of type one.