Talk given on December 1, 2021 on Zoom. A Colloquium talk given at Queensborough Community College Mathematics Department.

Abstract: Often in maths, insights from one area can provide inspiration in another. Formalizing analogies between different areas has resulted in the creation of whole new subfields and deep conjectures. A tool for this transfer process, which historically has been important in algebraic geometry, is topos theory, for the following very accessible reason: there are many ways to build toposes!  

In this talk, we shall describe two ways of building toposes, or more precisely two classes of Grothendieck topos: toposes of sheaves on topological spaces, and toposes of actions of discrete monoids. These classes are as different as can be, in the sense that the only topos which is in both classes is the topos of sets (corresponding to the one-point space and the trivial monoid, respectively). In spite of this, we can translate ideas from topology to algebra through these toposes by considering…

卷一 猫论

A home for all who love categories.

A home for all who love categories.