Definition & Meaning | English word COCOMPLETE

Definitions of COCOMPLETE

1. (math, of a category) In which all small colimits exist.

Examples of Using COCOMPLETE in a Sentence

• Dually, a category is cocomplete if and only if it has coequalizers and all (small) coproducts, or, equivalently, pushouts and coproducts.
• Characterization as colimit: Dually, if X is cocomplete and C is small, then the coend can be described as the coequalizer in the diagram.
• Quillen model categories are homotopically complete and cocomplete, and come with a built-in Eckmann–Hilton duality.
• For example, under this assumption, a poset may be defined as a small posetal category, a distributive lattice as a small posetal distributive category, a Heyting algebra as a small posetal finitely cocomplete cartesian closed category, and a Boolean algebra as a small posetal finitely cocomplete *-autonomous category.
• The category Meas is both complete and cocomplete, which means that all small limits and colimits exist in Meas.

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