elements-infinity-cats

Model-independent foundations for ∞-categories provide axioms and constructions that work across multiple presentations—such as quasi-categories, Segal spaces, or complete Segal spaces—without commitment to a single model. This enables reasoning about ∞-categorical structures through formal signatures and verification commands that hold universally.

Use the ∞-cosmos framework to define and check structures like isofibrations, comma ∞-categories, and adjunctions across any model presentation. Run `just infinity-cosmos-check structure.rzk` to apply formal verification commands that confirm your construction satisfies core requirements.

Yes. The ∞-cosmos axioms enable model-agnostic construction of comma ∞-categories, slice objects, and cone constructions. Once defined in the model-independent framework, these structures and their related adjunctions hold regardless of the underlying ∞-categorical presentation you choose.

Model-dependent definitions tie adjunctions to a specific ∞-category model, requiring re-verification for each presentation. Model-independent definitions establish adjunction data through formal signatures that work uniformly across all models satisfying the ∞-cosmos axioms, reducing redundancy and increasing portability.

Advanced understanding of category theory and ∞-categories is expected. The framework targets researchers and practitioners already working with multiple ∞-categorical models who need formal, reusable definitions across presentations rather than beginners new to the subject.

The framework covers objects, mapping spaces, isofibrations, comma objects, slices, and adjunction data. Each satisfies formal signatures and can be verified using model-independent commands, ensuring your constructions hold consistently across any ∞-cosmos model.