6 citations · 11 across the 9 of their papers we have counts for
12 papers
A counterexample to Kanalas' problem of continuously realising types
Morgan Rogers, Joshua Wrigley
We give an example of a coherent theory, a topological space, and a continuous assignment of the (model-theoretic) types of the theory to the points of the space, such that there i…
What is a monoid?
Paul Blain Levy, Morgan Rogers
In many situations one encounters an entity that resembles a monoid. It consists of a carrier and two operations that resemble a unit and a multiplication, subject to three equatio…
From free idempotent monoids to free multiplicatively idempotent rigs
Morgan Rogers
A multiplicatively idempotent rig (which we abbreviate to mirig) is a rig satisfying the equation . We show that a free mirig on finitely many generators is finite and com…
Topoi with enough points
Ivan Di Liberti, Morgan Rogers
We extend Deligne's original argument showing that locally coherent topoi have enough points, clarified using collage diagrams. We show that our refinement of Deligne's technique c…
Geometric morphisms between toposes of monoid actions: factorization systems
Jens Hemelaer, Morgan Rogers
Let M, N be monoids, and PSh(M), PSh(N) their respective categories of right actions on sets. In this paper, we systematically investigate correspondences between properties of geo…
Toposes of Monoid Actions
Morgan Rogers
We study toposes of actions of monoids on sets. We begin with ordinary actions, producing a class of presheaf toposes which we characterize. As groundwork for considering topologic…
Toposes of Topological Monoid Actions
Morgan Rogers
We demonstrate that categories of continuous actions of topological monoids on discrete spaces are Grothendieck toposes. We exhibit properties of these toposes, giving a solution t…
On Supercompactly and Compactly Generated Toposes
Morgan Rogers
We present and characterize the classes of Grothendieck toposes having enough supercompact objects or enough compact objects. In the process, we examine the subcategories of superc…
Solution to a problem by FitzGerald
Jens Hemelaer, Morgan Rogers
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 th…
An essential, hyperconnected, local geometric morphism that is not locally connected
Jens Hemelaer, Morgan Rogers
We give an example of an essential, hyperconnected, local geometric morphism that is not locally connected, arising from our work-in-progress on geometric morphisms $\mathbf{PSh}(M…
Monoid Properties as Invariants of Toposes of Monoid Actions
Jens Hemelaer, Morgan Rogers
We systematically investigate, for a monoid , how topos-theoretic properties of , including the properties of being atomic, strongly compact, local, totally con…
Toposes of Discrete Monoid Actions
Morgan Rogers
Properties of toposes of right -sets are studied, and these toposes are characterised up to equivalence by their canonical points. The solution to the corresponding Morita equiv…