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fix typos

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spiceghello 2018-04-10 10:41:57 +02:00 committed by Floris van Doorn
parent d2c7eb2368
commit f835dc896e
2 changed files with 3 additions and 3 deletions
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2
.gitignore vendored
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@ -47,7 +47,7 @@ build.ninja
# these rules might exclude image files for figures etc. # these rules might exclude image files for figures etc.
# *.ps # *.ps
# *.eps # *.eps
# *.pdf *.pdf
## Generated if empty string is given at "Please type another file name for output:" ## Generated if empty string is given at "Please type another file name for output:"
.pdf .pdf

4
Notes/smash.tex
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@ -216,7 +216,7 @@ We define the pointed equivalences:
\begin{lem}\label{lem:smash-general} \begin{lem}\label{lem:smash-general}
The smash product is functorial: if $f:A\pmap A'$ and $g:B\pmap B'$ then The smash product is functorial: if $f:A\pmap A'$ and $g:B\pmap B'$ then
$f\smsh g:A\smsh B\pmap A'\smsh B'$. We write $A\smsh g$ or $f\smsh B$ if one of the $f\smsh g:A\smsh B\pmap A'\smsh B'$. We write $A\smsh g$ or $f\smsh B$ if one of the
functions is the identity function. Moreover, if $p:f\sim f'$ and $q:g\sim g'$ then $p\smsh q:f\smsh g\sim f'\smsh g'$; this operation preserves reflexivities, symmetries and transitivies. We will write $p \smsh g$ or $f \smsh q$ if one of the homotopies is reflexivity. functions is the identity function. Moreover, if $p:f\sim f'$ and $q:g\sim g'$ then $p\smsh q:f\smsh g\sim f'\smsh g'$; this operation preserves reflexivities, symmetries and transitivities. We will write $p \smsh g$ or $f \smsh q$ if one of the homotopies is reflexivity.
% The smash product satisfies the following properties. % The smash product satisfies the following properties.
% \begin{itemize} % \begin{itemize}
% \item The smash product is functorial: if $f:A\pmap A'$ and $g:B\pmap B'$ then % \item The smash product is functorial: if $f:A\pmap A'$ and $g:B\pmap B'$ then
@ -729,7 +729,7 @@ are filled by (corollaries of) \autoref{lem:smash-general}.
$\epsilon_{B,C}\equiv\epsilon : (B\pmap C)\smsh B \pmap C$ dinatural in $B$ and pointed natural in $C$. $\epsilon_{B,C}\equiv\epsilon : (B\pmap C)\smsh B \pmap C$ dinatural in $B$ and pointed natural in $C$.
These maps satisfy the unit-counit laws: These maps satisfy the unit-counit laws:
$$(A\to\epsilon_{A,B})\o \eta_{A\to B,A}\sim \idfunc[A\to B]\qquad $$(A\to\epsilon_{A,B})\o \eta_{A\to B,A}\sim \idfunc[A\to B]\qquad
\epsilon_{B,B\smsh C}\o \eta_{A,B}\smsh B\sim\idfunc[A\smsh B].$$ \epsilon_{B,A\smsh B}\o \eta_{A,B}\smsh B\sim\idfunc[A\smsh B].$$
\end{lem} \end{lem}
Note: $\eta$ is also dinatural in $B$, but we don't need this. Note: $\eta$ is also dinatural in $B$, but we don't need this.
\begin{proof} \begin{proof}