List questions from functors

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Why $\Psi\circ\Phi=1$ in Yoneda lemma?

Published on 25 Mar 2026 - 21:47

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Associativity of cup product in Homology

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definition of "closed monoidal functor"

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Are there any "distinguished" points in the category of smooth manifolds?

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Name for a alternative version of the image of a functor

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On the monadicity of Cat

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Notation in Katz-Mazur Arithmetic Moduli of Elliptic Curves

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255

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Natural Transformation of Bifunctors

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Reference for the category of functors from finite sets with surjections to abelian groups

Published on 31 Oct 2021 - 4:49

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Problem with functor category notation

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Let $F:\mathcal{A}\to\mathcal{B}$ be a fully faithful covariant functor. Then, if $F(f):F(A_1)\to F(A_2)$ is an isomorphism, so is $f:A_1\to A_2$.

Published on 27 Mar 2026 - 17:06

99

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If $A \in \text{R-MOD}$, then $\text{Hom}_R(A,-)$ is left exact.

Published on 19 Nov 2021 - 10:01

205

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Definition of the cotensor in sSet

Published on 25 Mar 2026 - 5:06

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Exercise 1.5.xi from Emily Riehl's "Category Theory in Context" on properties of some functors

Published on 27 Nov 2021 - 21:00

List Question

On reduced functors and closed complements of open subfunctors

Why $\Psi\circ\Phi=1$ in Yoneda lemma?

Associativity of cup product in Homology

definition of "closed monoidal functor"

Are there any "distinguished" points in the category of smooth manifolds?

Name for a alternative version of the image of a functor

On the monadicity of Cat

Notation in Katz-Mazur Arithmetic Moduli of Elliptic Curves

Natural Transformation of Bifunctors

Reference for the category of functors from finite sets with surjections to abelian groups

Problem with functor category notation

Let $F:\mathcal{A}\to\mathcal{B}$ be a fully faithful covariant functor. Then, if $F(f):F(A_1)\to F(A_2)$ is an isomorphism, so is $f:A_1\to A_2$.

If $A \in \text{R-MOD}$, then $\text{Hom}_R(A,-)$ is left exact.

Definition of the cotensor in sSet

Exercise 1.5.xi from Emily Riehl's "Category Theory in Context" on properties of some functors

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