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- Publications
- Influence
Toposes of Discrete Monoid Actions
- M. Rogers
- Mathematics
- 24 May 2019
Properties of toposes of right $M$-sets are studied, and these toposes are characterised up to equivalence by their canonical points. The solution to the corresponding Morita equivalence problem is… Expand
An essential, hyperconnected, local geometric morphism that is not locally connected.
- Jens Hemelaer, M. Rogers
- Mathematics
- 25 September 2020
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) \to… Expand
Solution to a problem by FitzGerald
- Jens Hemelaer, M. Rogers
- Mathematics
- 24 November 2020
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 that these conditions… Expand
On Supercompactly and Compactly Generated Toposes
- M. Rogers
- Mathematics
- 11 January 2021
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 supercompact objects and… Expand
Monoid Properties as Invariants of Toposes of Monoid Actions
- Jens Hemelaer, M. Rogers
- Mathematics
- 22 April 2020
We systematically investigate, for a monoid $M$, how topos-theoretic properties of $\mathbf{PSh}(M)$, including the properties of being atomic, strongly compact, local, totally connected or cohesive,… Expand