Definition of Colimit. Meaning of Colimit. Synonyms of Colimit

Here you will find one or more explanations in English for the word Colimit. Also in the bottom left of the page several parts of wikipedia pages related to the word Colimit and, of course, Colimit synonyms and on the right images related to the word Colimit.

Definition of Colimit

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Meaning of Colimit from wikipedia

- notion of a colimit generalizes constructions such as disjoint unions, direct sums, coproducts, pushouts and direct limits. Limits and colimits, like the...
- homotopy limit and colimitpg 52 are variants of the notions of limit and colimit extended to the homotopy category Ho ( Top ) {\displaystyle {\text{Ho}}({\textbf...
- w:j\to k} such that w u = w v {\displaystyle wu=wv} . A filtered colimit is a colimit of a functor F : J → C {\displaystyle F:J\to C} where J {\displaystyle...
- sends each diagram to its limit. Dually, the colimit of diagram D is a universal cone from D. If the colimit exists for all diagrams of type J one has a...
- characterised as a terminal object in the category of cones to F. Likewise, a colimit of F may be characterised as an initial object in the category of co-cones...
- theory, a branch of mathematics, a limit or a colimit of presheaves on a category C is a limit or colimit in the functor category C ^ = F c t ( C op ,...
- system of homomorphisms. Direct limits are a special case of the concept of colimit in category theory. Direct limits are dual to inverse limits, which are...
- ind-completion or ind-construction is the process of freely adding filtered colimits to a given category C. The objects in this ind-completed category, denoted...
- : D → Set {\displaystyle G:D\to {\textbf {Set}}} , the colimit of G is the same as the colimit of G ∘ F {\displaystyle G\circ F} . Note that an object...
- axiom of choice. Similar remarks apply to the colimit functor (which ****igns to every functor its colimit, and is covariant). Power sets functor The power...