An Essential,Hyperconnected, Local Geometric Morphism that is not Locally Connected

Applied Categorical Structures - Thomas Streicher asked on the category theory mailing list whether every essential, hyperconnected, local geometric morphism is automatically locally connected. We...     

Solution to a problem of FitzGerald

Semigroup Forum - FitzGerald identified four conditions (RI), (UR), (RI*) and (UR*) that are necessarily satisfied by an algebra if its monoid of endomorphisms has commuting idempotents. We show...     

Monoid Properties as Invariants of Toposes of Monoid Actions

Applied Categorical Structures - We systematically investigate, for a monoid M, how topos-theoretic properties of $${{\,\mathrm{\mathbf {PSh}}\,}}(M)$$ , including the properties of being atomic,...