Geometric morphisms are a central concept in topos theory, serving as structure-preserving maps between topoi that reflect the relationships between their categorical structures. They consist of a pair of functors that relate two topoi, typically referred to as the direct and inverse image functors, which allow for the transfer of information between different contexts while maintaining the underlying logical framework. This concept plays a crucial role in understanding algebraic theories and cohomology theories as it provides a way to compare and relate different topoi within these frameworks.
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