User:Silvermatsu/sandbox

memo a

Hartshorne, Robin (1970). Ample Subvarieties of Algebraic Varieties. Lecture Notes in Mathematics. Vol. 156. doi:10.1007/BFb0067839. ISBN 978-3-540-05184-8.

https://books.google.com/books?id=okHfUv4l4vgC&pg=PA57

• https://books.google.com/books?id=7z4mBQAAQBAJ&pg=121
• https://books.google.com/books?id=7z4mBQAAQBAJ&pg=228

• https://books.google.com/books?id=nfpzBAAAQBAJ&pg=195
• https://books.google.com/books?id=vr8FCAAAQBAJ&pg=49
• https://books.google.com/books?id=MOAqeoYlBMQC&q=JP.+Serre%2C+%22Trees%22

memo d

Let $X_{1},\dots ,X_{n}\in C$. Let $P_{1},P_{2}$ be arbitrary two parenthesized products of $X_{1},\dots ,X_{n}$ (in this order) with arbitrary insertions of unit objects $1$. Let $f,g:P_{1}\rightarrow P_{2}$ be two isomorphisms, obtained by composing associativity and unit isomorphisms and their inverses possibly tensored with identity morphisms. Then $f=g$.

strictification

• Schauenburg, Peter (2001). "Turning monoidal categories into strict ones". The New York Journal of Mathematics [Electronic Only]. 7: 257–265. ISSN 1076-9803.

• Mac Lane, Saunders (1998). Categories for the working mathematician. New York: Springer. ISBN 0-387-98403-8. OCLC 37928530.

Mac Lane, Saunders (1978). "Symmetry and Braidings in Monoidal Categories". Categories for the Working Mathematician. Graduate Texts in Mathematics. Vol. 5. pp. 251–266. doi:10.1007/978-1-4757-4721-8_12. ISBN 978-1-4419-3123-8. §3. Strict Monoidal Categories,

memo i

In monoidal category $C$, the following two conditions are called coherence conditions:

• Let a bifunctor $\otimes \colon \mathbf {C} \times \mathbf {C} \to \mathbf {C}$ called the tensor product, a natural isomorphism $\alpha _{A,B,C}$, called the associator:

$\alpha _{A,B,C}\colon (A\otimes B)\otimes C\rightarrow A\otimes (B\otimes C)$

• Also, let $I$ an identity object and $I$ has a left identity, a natural isomorphism $\lambda _{A}$ called the left unitor:

$\lambda _{A}:I\otimes A\rightarrow A$

as well as, let $I$ has a right identity, a natural isomorphism $\rho _{A}$ called the right unitor:

$\rho _{A}:A\otimes I\rightarrow A$.