List questions from hom-functor | MathQa

Is there a reason why we call $\mathrm{Hom}(A, -)$ covariant and $\mathrm{Hom}(-,B)$ contravariant?

Published on 12 Jan 2025 - 19:13

Exactness of a sequence in Abelian category

Published on 03 Jan 2025 - 10:43

Difference between functors $\text{Hom}_B(-,B)$ and $\text{Hom}_{\mathbb C}(-,\mathbb C)$

Published on 02 Jan 2025 - 23:20

There is a unique map $P \to \text{Hom}(A, \prod_i C_i)$ whenever $P \xrightarrow{p_i} \text{Hom}(A, C_i)$?

Published on 02 Jan 2025 - 19:24

What is the name of this identity relating the monoidal products of finite sets and finite-dimensional vector spaces?

Published on 03 Jan 2025 - 12:09

Showing that $H_A\simeq H_{A'}$ implies $A\simeq A'$

Published on 03 Jan 2025 - 6:31

Lifting of a morphism in a hom-functor when hom-sets are empty

Published on 03 Jan 2025 - 0:06

What is a clear, elegant proof that $\text{Hom}(\cdot, Y)$ is a right-exact functor in a category of modules?

Published on 27 Dec 2024 - 13:23

Hom functors preserve fibre products.

Published on 27 Dec 2024 - 6:25

Yoneda lemma, wrong direction, weighted colimit

Published on 26 Dec 2024 - 23:48