26 citations · 102 across the 23 of their papers we have counts for
25 papers
From Grothendieck cofibrations to factorization systems: a formal 2-monadic account
Fernando Lucatelli Nunes, Walter Tholen
Grothendieck cofibrations describe transport in a category varying over a base, while factorization systems organize the arrows of a category into two complementary classes. We giv…
The normal decomposition of a morphism in categories without zeros
Renier Jansen, Muhammad Qasim, Walter Tholen
For a morphism f in a category C with sufficiently many finite limits and colimits, we discuss an elementary construction of a decomposition of f through objects P and N which, if…
Smallness in Topology
Jiri Adamek, Miroslav Husek, Jiri Rosicky +1
Quillen's notion of small object and the Gabriel-Ulmer notion of finitely presentable or generated object are fundamental in homotopy theory and categorical algebra. Do these notio…
Groupoids and skeletal categories form a pretorsion theory in
Francis Borceux, Federico Campanini, Marino Gran +1
We describe a pretorsion theory in the category of small categories: the torsion objects are the groupoids, while the torsion-free objects are the skeletal categories, i.e.,…
A categorical review of complete regularity
Amir Homayoun Nejah, Walter Tholen
We use the ultrafilter-convergence axiomatics for topological spaces to motivate in detail a gentle categorical introduction, first to Barr's Set-based relational T-algebras, and t…
Kan extensions are partial colimits
Paolo Perrone, Walter Tholen
One way of interpreting a left Kan extension is as taking a kind of "partial colimit", whereby one replaces parts of a diagram by their colimits. We make this intuition precise by…