### Some articles on *colimits*:

Limit (category Theory) - Functors and Limits - Examples

... Hom functors need not preserve

... Hom functors need not preserve

**colimits**... functor C → Set preserves limits (but not necessarily**colimits**) ... The forgetful functor U Grp → Set creates (and preserves) all small limits and filtered**colimits**however, U does not preserve coproducts ...Topos - Grothendieck Topoi (topoi in Geometry) - Equivalent Definitions - Giraud's Axioms

... a small set of generators, and admits all small

... a small set of generators, and admits all small

**colimits**... Furthermore,**colimits**commute with fiber products ... Since C has**colimits**we may form the coequalizer of the two maps R→X call this X/R ...Category Of Rings - Properties - Limits and

... Ring is both complete and cocomplete, meaning that all small limits and

**Colimits**... Ring is both complete and cocomplete, meaning that all small limits and

**colimits**exist in Ring ... forgetful functor U Ring → Set creates (and preserves) limits and filtered**colimits**, but does not preserve either coproducts or coequalizers ... Examples of limits and**colimits**in Ring include The ring of integers Z forms an initial object in Ring ...Limit (category Theory) - Examples -

... Examples of

**Colimits**... Examples of

**colimits**are given by the dual versions of the examples above Initial objects are**colimits**of empty diagrams ... Coproducts are**colimits**of diagrams indexed by discrete categories ... Copowers are**colimits**of constant diagrams from discrete categories ...Category Of Topological Spaces - Limits and

... The category Top is both complete and cocomplete, which means that all small limits and

**Colimits**... The category Top is both complete and cocomplete, which means that all small limits and

**colimits**exist in Top ... → Set uniquely lifts both limits and**colimits**and preserves them as well ... Dually,**colimits**in Top are obtained by placing the final topology on the corresponding**colimits**in Set ...Main Site Subjects

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