9 citations · 9 across the 3 of their papers we have counts for
5 papers · 1 filter
Grothendieck quantaloids for allegories of enriched categories
Hans Heymans, Isar Stubbe
For any small involutive quantaloid Q we define, in terms of symmetric quantaloid-enriched categories, an involutive quantaloid Rel(Q) of Q-sheaves and relations, and a category Sh…
Elementary characterisation of small quantaloids of closed cribles
Hans Heymans, Isar Stubbe
Each small site (C,J) determines a small quantaloid of closed cribles R(C,J). We prove that a small quantaloid Q is equivalent to R(C,J) for some small site (C,J) if and only if th…
Symmetry and Cauchy completion of quantaloid-enriched categories
Hans Heymans, Isar Stubbe
We formulate an elementary condition on an involutive quantaloid Q under which there is a distributive law from the Cauchy completion monad over the symmetrisation comonad on the c…
Modules on involutive quantales: canonical Hilbert structure, applications to sheaf theory
Hans Heymans, Isar Stubbe
We explain the precise relationship between two module-theoretic descriptions of sheaves on an involutive quantale, namely the description via so-called Hilbert structures on modul…
On principally generated Q-modules in general, and skew local homeomorphisms in particular
Hans Heymans, Isar Stubbe
Ordered sheaves on a small quantaloid Q have been defined in terms of Q-enriched categorical structures; they form a locally ordered category Ord(Q). The free-cocompletion KZ-doctr…