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15
216
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When can functors fail to be adjoints if their hom sets are bijective?

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#category-theory #adjoint-functors #functors #yoneda-lemma #hom-functor
152
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Existence of morphisms in a free completion under directed colimits,$\lambda$-accessible category

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#category-theory #limits-colimits #monomorphisms #hom-functor #accessible-categories
216
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Preservation of limits by representable functors

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#category-theory #limits-colimits #functors #hom-functor
132
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There is a natural morphism $\lim\limits_{\longleftarrow} \beta \to \lim\limits_{\longleftarrow} \beta \circ \varphi^{op}$?

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#category-theory #limits-colimits #functors #hom-functor
112
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Fully faithful nerve ⟹ injective on objects?

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#category-theory #functors #hom-functor
358
Views

$\operatorname{Hom}$ functor is projective?

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#abstract-algebra #category-theory #hom-functor
120
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Nearly locally presentable categories

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#category-theory #functors #representable-functor #hom-functor #locally-presentable-categories
632
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Existence of injective homomorphism

Published on
#category-theory #abelian-groups #hom-functor
267
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Isomorphism between Hom-space and $k$

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#vector-spaces #category-theory #hom-functor
1.2k
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Is “monoidal category enriched over itself” the same as “closed monoidal category”?

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#category-theory #examples-counterexamples #adjoint-functors #monoidal-categories #hom-functor
113
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Does an adjoint of an internal Hom functor of a prounital closed category define a tensor product?

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#category-theory #examples-counterexamples #adjoint-operators #monoidal-categories #hom-functor
85
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Currying in a locally small category with coproducts

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#category-theory #tensor-products #adjoint-functors #functors #hom-functor
87
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decomposition of hom-functors in a self-enriched category

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#abstract-algebra #category-theory #monoidal-categories #enriched-category-theory #hom-functor
49
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How to see that $S(\sigma) = \text{Hom}_{\Delta}(\sigma, [0,1])$ maps to the category $\tilde{\Delta}^{\text{op}}$.

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#category-theory #simplicial-stuff #functors #hom-functor
143
Views

The Yoneda lemma and a natural bijection

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#elementary-set-theory #category-theory #yoneda-lemma #representable-functor #hom-functor

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