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• Tags
  • #higher-algebra
• Refs:
  • #todo/add-references
• Links:
  • kappa filtered

Ind objects

\({\mathsf{Ind}}(\mathsf{C})\) is the category of formal filtered colimits (“inductive systems”) of objects in \(\mathsf{C}\). How to do this: take the free cocompletion \(\mathsf{C} \to [\mathsf{C}, {\mathsf{Set}}]\) and compute the colimit there.

Pro objects

\({\mathsf{Pro}}\mathsf{C}\) is the category of formal limits (“projective systems”) of objects in \(\mathsf{C}\). Take the free completion \(\mathsf{C} \to { { [\mathsf{C}, {\mathsf{Set}}] }^{\operatorname{op}}}\)