Skip to content

Commit

Permalink
notes
Browse files Browse the repository at this point in the history
  • Loading branch information
BostX committed Feb 21, 2024
1 parent 6725069 commit 6b69005
Show file tree
Hide file tree
Showing 2 changed files with 14 additions and 8 deletions.
18 changes: 12 additions & 6 deletions category-theory.org
Original file line number Diff line number Diff line change
Expand Up @@ -100,11 +100,14 @@ No matter which way you go around you get the same thing.
\bigskip

_Cartesian Closed Category CCC_ - useful in programming
- Cartesian: has product $A \cprod B$ for any pair of objects $A$, $B$
- Closed: has exponential $B^A$, i.e. morphisms $A \to B$ for any pair of
objects $A$, $B$
- Cartesian:
for any two objects $A$, $B$ of a category $\mathcal{C}$ there exists an
ordered pair in $\mathcal{C}$ called product, noted as $A \cprod B$.
- Closed:
for any two objects $A$, $B$ there exists a morphisms $A \to B$ in
$\mathcal{C}$ called exponential, notes as $B^A$.
- 0-th power of an obj: has terminal obj $\termObj$ (for all objects there
exists a unique map $A \to \termObj$)
exists a unique morphism $A \to \termObj$)
- multiplying by terminal obj $\termObj$ gives back the original obj
- initial obj $\initObj$ - dual to terminal obj $\termObj$; Top and Bottom
objects i.e. any one-element set (= singleton) is terminal DTTO for poset 1 is
Expand Down Expand Up @@ -518,8 +521,11 @@ the NaT is transported from this point.
- Adjoints / adjoint functors - functors with a relation of adjunction between
them.

If $\Fun{F}$ is (left) adjoint to $\Fun{G}$, then there is typically some
formula of the type $(x, \Fun{G}y) \iso (\Fun{F}x, y)$.
\\

If $\Fun{F}$ is (left) adjoint to $\Fun{G}$ and $\Fun{G}$ is (right) adjoint
to $\Fun{F}$, then there is typically some formula of the type $(x, \Fun{G}y)
\iso (\Fun{F}x, y)$.

\bigskip

Expand Down
4 changes: 2 additions & 2 deletions notes/guix-guile-nix/guix_package.scrbl
Original file line number Diff line number Diff line change
Expand Up @@ -184,8 +184,8 @@
set --export GUIX_PACKAGE_PATH $lp/bost/packages/patches
guix build --load-path=$lp --keep-failed emacs-spacemacs

# build the packages' source derivations
guix build --expression='(@"@"@"@" (bost packages emacs-xyz) emacs-color-identifiers-mode)' --source
# build the packages' source derivations: the [at] char must be used twice
guix build --expression='(@"@"@"@" (bost gnu packages emacs-xyz) emacs-color-identifiers-mode)' --source
}

@block{@block-name{Garbage collection}
Expand Down

0 comments on commit 6b69005

Please sign in to comment.