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A universal cone to a diagram, simultaneously generalizing products, equalizers, pullbacks, and inverse limits.
wp-finitely-complete-categoryriehl-category-contextEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
A cartesian category has finite products, which are limits of finite discrete diagrams, including a terminal object as the empty product.
Pass canonically from a stronger object to structure it determines, or forget part of the data while retaining a valid weaker structure. The carrier may change under a canonical induced construction.
wp-cartesian-categoryriehl-category-contextThis is an authored directed relation from the source endpoint to the target endpoint.
A finitely complete category has limits for every finite diagram; forgetting the ambient axiom leaves individual categorical limits.
Pass canonically from a stronger object to structure it determines, or forget part of the data while retaining a valid weaker structure. The carrier may change under a canonical induced construction.
nlab-finite-limitsriehl-category-contextThis is an authored directed relation from the source endpoint to the target endpoint.
A diagram is a functor into a category; when a universal cone exists, its apex is the limit of that diagram.
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
riehl-category-contextEach relation below starts at this concept.
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