mathlib documentation

category_theory.limits.shapes.finite_limits

Categories with finite limits. #

A typeclass for categories with all finite (co)limits.

We can always derive has_finite_limits C by providing limits at an arbitrary universe.

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A category has all finite colimits if every functor J ⥤ C with a fin_category J instance and J : Type has a colimit.

This is often called 'finitely cocomplete'.

Instances of this typeclass

We can always derive has_finite_colimits C by providing colimits at an arbitrary universe.

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has_finite_wide_pullbacks represents a choice of wide pullback for every finite collection of morphisms

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has_finite_wide_pushouts represents a choice of wide pushout for every finite collection of morphisms

Finite wide pullbacks are finite limits, so if C has all finite limits, it also has finite wide pullbacks

Finite wide pushouts are finite colimits, so if C has all finite colimits, it also has finite wide pushouts