Everything about Direct limit
Special case of colimit in category theory
In mathematics, a direct limit is a way to construct a object from many objects that are put together in a specific way. These objects may be groups, rings, vector spaces or in general objects from any category. The way they are put together is specified by a system of homomorphisms between those smaller objects. The direct limit of the objects, where ranges over some directed set, is denoted by. This notation suppresses the system of homomorphisms; however, the limit depends on the system of homomorphisms. Wikipedia ā
š§ Start here: a 6-step reading path
- Read the overview: Direct limitA 5-minute orientation
- Skim a recent paper: Does foreign direct investment limit trade-adjusted carbon emissions: fresh evidence from global dataInfluential work since 2022
- Pick up a classic book: Financing a theatrical productionThe most-reprinted book on the subject
- Read the landmark paper: Direct Experimental Limit on NeutronāMirror-Neutron OscillationsCited 83 times
- Go sideways: Inverse limitA closely related topic
- Go sideways: Limit (category theory)A closely related topic
š Definitions
Noun A set of equivalence classes which partition the disjoint union of the members of a direct system; each equivalence class being a sort of ādrainage basinā of the mappings (of the morphisms) of the direct system, if these are analogically considered as āriversā. (If iā¤k, jā¤k in the indexing poset, then there exist fik:AiāAk and fjk:AjāAk. If aiāAi, ajāAj such that fik(ai)=fjk(aj) then aiā¼aj. If k = j then fjj(aj)=aj, fij(ai)=aj.)
Noun a colimit
šļø The subject at a glance
š Landmark papers (most cited)
Direct Experimental Limit on NeutronāMirror-Neutron Oscillations
A Direct Method on the Evaluation of Ratchet Limit
Inductive limit and infinite direct product of operator algebras
Subgroups of direct products of limit groups
The direct limit closure of perfect complexes
Direct calculation of reactive power limit points
Direct and subdiffraction-limit laser nanofabrication in silicon
Direct limit analysis via rigid-plastic finite elements
š Influential since 2022
Does foreign direct investment limit trade-adjusted carbon emissions: fresh evidence from global data
Expanded Limit Boundary Explicit Model Predictive Direct Speed Control for PMSMs
First direct limit on the 334 keV resonance strength in $$^{22}$$Ne($$\alpha $$,$$\gamma $$)$$^{26}$$Mg reaction
Highly stable bismuth-chloride perovskite X-ray direct detectors with an ultralow detection limit
Compact Model and Detailed Balance Limit for a Dual nāType Direct ZāScheme Heterojunction
š Books worth reading
- šFinancing a theatrical productionFederal Bar Association of New York, New Jersey, and Connecticut. Committee on the Law of the Theatre. Ā· 1964
Latex and lingerieMerl Storr Ā· 2003
A Treatise on Mechanics, Applied to the Arts: Including Statics and HydrostaticsHenry Moseley , Society for the promotion of Christian knowledge Committee of general literature and education Ā· 1847
Arrow through the heartGreig Stewart Ā· 1998
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
š Related topics
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