# The category of topological spaces has all limits and colimits #

Further, these limits and colimits are preserved by the forgetful functor --- that is, the underlying types are just the limits in the category of types.

def TopCat.limitCone {J : Type v} (F : ) :

A choice of limit cone for a functor F : J ⥤ TopCat. Generally you should just use limit.cone F, unless you need the actual definition (which is in terms of Types.limitCone).

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def TopCat.limitConeInfi {J : Type v} (F : ) :

A choice of limit cone for a functor F : J ⥤ TopCat whose topology is defined as an infimum of topologies infimum. Generally you should just use limit.cone F, unless you need the actual definition (which is in terms of Types.limitCone).

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The chosen cone TopCat.limitCone F for a functor F : J ⥤ TopCat is a limit cone. Generally you should just use limit.isLimit F, unless you need the actual definition (which is in terms of Types.limitConeIsLimit).

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The chosen cone TopCat.limitConeInfi F for a functor F : J ⥤ TopCat is a limit cone. Generally you should just use limit.isLimit F, unless you need the actual definition (which is in terms of Types.limitConeIsLimit).

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def TopCat.colimitCocone {J : Type v} (F : ) :

A choice of colimit cocone for a functor F : J ⥤ TopCat. Generally you should just use colimit.cocone F, unless you need the actual definition (which is in terms of Types.colimitCocone).

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The chosen cocone TopCat.colimitCocone F for a functor F : J ⥤ TopCat is a colimit cocone. Generally you should just use colimit.isColimit F, unless you need the actual definition (which is in terms of Types.colimitCoconeIsColimit).

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The terminal object of Top is PUnit.

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The terminal object of Top is PUnit.

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The initial object of Top is PEmpty.

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The initial object of Top is PEmpty.

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