57 Citations
RESTRICTED ADJOINTS AND TOPOLOGICAL FUNCTORS
- Mathematics
- 1983
Abstract The idea of adjoint functors or adjoint situation is one of the most important concepts in category theory. However, many examples are known which deviate from adjoint situations in one…
On topological algebras relative to full and faithful dense functors
- Mathematics
- 1976
In this paper I consider algebras in the sense of Diers ([5]) in topological categories ([~, [~, [I~, [I~ , [I~, [I~, ~, [18], [I~, [20], ~, ~5] ). This notion of an algebra generalizes at the same…
A Relationship between Left Exact and Representable Functors
- MathematicsCanadian Journal of Mathematics
- 1971
Our aim in this paper is to demonstrate a relationship between left exact and representable functors. More precisely, in the functor category whose objects are the additive functors from the dual of…
Codensity and the ultrafilter monad
- Mathematics
- 2012
Even a functor without an adjoint induces a monad, namely, its codensity monad; this is subject only to the existence of certain limits. We clarify the sense in which codensity monads act as…
$\mathbf{Z}$-Categories I
- Mathematics
- 2022
This paper is the first in a series of two papers, Z-Categories I and Z-Categories II, which develop the notion of Z-category, the natural bi-infinite analog to strict ω-categories, and show that the…
CODENSITY AND THE ULTRAFILTER MONAD
- Mathematics
- 2013
Even a functor without an adjoint induces a monad, namely, its codensity monad; this is subject only to the existence of certain limits. We clarify the sense in which codensity monads act as…