Lex colimits (Q456823)
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scientific article; zbMATH DE number 6094125
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Lex colimits |
scientific article; zbMATH DE number 6094125 |
Statements
Lex colimits (English)
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16 October 2012
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The paper develops a theory of finitely complete categories with colimits of special type and of ``exactness conditions'' relating finite limits and specified colimits. The notion can be understood as a form of cocompleteness in the \(2\)-category of finitely complete catgories and finite-limit-preserving functors. The notion generalizes finitely presentable categories, regular categories, Barr-exact categories, lextensive categories, coherent categories and adhesive categories. These examples are particular instances of a given general notion. An embedding of these small categories into small-exact categories is described. Finally, a relative completion in general theory is given.
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finitely complete category
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finite-limit-preserving functor
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topoi
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exact category
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specified cocompleteness
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