Definition of Colimit. Meaning of Colimit. Synonyms of Colimit

- 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...
- 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...
- 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 ,...
- 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...
- coproduct or fibered sum or cocartesian square or amalgamated sum) is the colimit of a diagram consisting of two morphisms f : Z → X and g : Z → Y with 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...
- and small colimits. See limit and colimit of presheaves for further discussion. The density theorem states that every presheaf is a colimit of representable...
- limit becomes a direct limit or inductive limit, and a limit becomes a colimit. We start with the definition of an inverse system (or projective system)...