A depth-bounded naturality meta-operation in the Catt type theory constructs and machine-checks cylinder and cone composites in weak omega-categories.
Computads and slices of operads
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abstract
For a given $\omega$-operad $A$ on globular sets we introduce a sequence of symmetric operads on $Set$ called slices of $A$ and show how the connected limit preserving properties of slices are related to the property of the category of $n$-computads of $A$ being a presheaf topos.
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Naturality for higher-dimensional path types
A depth-bounded naturality meta-operation in the Catt type theory constructs and machine-checks cylinder and cone composites in weak omega-categories.