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In category theory, a branch of mathematics, an initial object of a category C is an object I in C such that for every object X in C, there exists precisely one morphism I → X. The dual notion is that of a terminal object (also called terminal element): T is terminal if for every object X in C there exists exactly one morphism X → T.
Examples of limits and colimits in Top include: The empty set (considered as a topological space) is the initial object of Top; any singleton topological space is a terminal object. There are thus no zero objects in Top. The product in Top is given by the product topology on the Cartesian product.
Some file managers implement a TUI (here: Midnight Commander) Vim is a very widely used TUI text editor. In computing, text-based user interfaces (TUI) (alternately terminal user interfaces, to reflect a dependence upon the properties of computer terminals and not just text), is a retronym describing a type of user interface (UI) common as an early form of human–computer interaction, before ...
The code for the math example reads: <math display= "inline" > \sum_{i=0}^\infty 2^{-i} </math> The quotation marks around inline are optional and display=inline is also valid. [2] Technically, the command \textstyle will be added to the user input before the TeX command is passed to the renderer. The result will be displayed without further ...
Limits and colimits in a category are defined by means of diagrams in .Formally, a diagram of shape in is a functor from to : :. The category is thought of as an index category, and the diagram is thought of as indexing a collection of objects and morphisms in patterned on .
The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [1] and the LaTeX symbol.
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The coequalizer of two ring homomorphisms f and g from R to S is the quotient of S by the ideal generated by all elements of the form f(r) − g(r) for r ∈ R. Given a ring homomorphism f : R → S the kernel pair of f (this is just the pullback of f with itself) is a congruence relation on R .
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