Questions tagged [limits-colimits]
For questions about categorical limits and colimits, including questions about (co)limits of general diagrams, questions about specific special kinds of (co)limits such as (co)products or (co)equalizers, and questions about generalizations such as weighted (co)limits and (co)ends.
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Existence of a Coend in a Monoidal Category
Let $B$ be a monoidal category with multiplication $\Box$. Let $P$ be a category and let $T \colon P^\mathrm{op} \to B$ and $S \colon P \to B$ be functors. MacLane [CWM, p226] says that these two ...
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The existence of ends of functors.
Let $\mathcal {C}$ be a small category. In MacLane's book we have a theorem:
If $\mathcal X$ is small complete and $\mathcal C$ is small, then every functor $S \colon \mathcal C^{\text op} \times \...
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Example of a functor which preserves all small limits but has no left adjoint
The General Adjoint Functor Theorem (Category Theory) states that for a locally small and complete category $D$, a functor $G\colon D \to C$ has a left adjoint if and only if $G$ preserves all small ...
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Looking for an example of a concrete calculation of a certain direct limit to get my hands dirty with generalized fractions
I am going to give a talk on the Koszul complex and its connection with local cohomology. We are using the book Residues and Duality for Projective Algebraic Varieties by Kunz and in the chapter that ...
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On limits, schemes and Spec functor
I have several related questions:
Do there exist colimits in the category of schemes? If not, do there exist just direct limits? Do there exist limits? If not, do there exist just inverse limits? With ...
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Right adjoints preserve limits
In Awodey's book I read a slick proof that right adjoints preserve limits. If $F:\mathcal{C}\to \mathcal{D}$ and $G:\mathcal{D}\to \mathcal{C}$ is a pair of functors such that $(F,G)$ is an adjunction,...
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Category-theoretic limit related to topological limit?
Is there any connection between category-theoretic term 'limit' (=universal cone) over diagram, and topological term 'limit point' of a sequence, function, net...?
To be more precise, is there a ...
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How to understand the "create limit"?
I find it is hard to understand the "create limit." (You can find it in Mac Lane's Categories for the working mathematician, P112; there it defines: "A functor $V:A→x$ creates limits for a functor $F:...
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In (relatively) simple words: What is an inverse limit?
I am a set theorist in my orientation, and while I did take a few courses that brushed upon categorical and algebraic constructions, one has always eluded me.
The inverse limit. I tried to ask one of ...
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Meaning of pullback
I was wondering if the following two
meanings of pullback are related and
how:
In terms of Precomposition with a function:
a function $f$ of a variable $y$, where $y$
itself is a function of ...
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