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Revision Browser : Enriched Category Theory
view 'Enriched Category Theory

diff 2010-11-07 15:44:19 - revision [ Version = 14 --> (current) ] by bci1
diff 2010-11-01 01:21:03 - revision [ Version = 13 --> Version 14 ] by bci1
diff 2010-11-01 01:18:06 - revision [ Version = 12 --> Version 13 ] by bci1
The connection with classical conical limits when $V = Set$ \subsection{Full subcategories and limits: the closure of a full subcategory} \subsection{Strongly generating functors} \subsection{Tensor and Cotensor Products} \subsection{Kan extensions} The definition of Kan extensions; their expressibility by limits and colimits \subsection{Iterated Kan extensions; Kan adjoints} \subsection{Filtered categories when $V = Set$} \subsection{General Representability and Adjoint Functor theorems} \subsection{Representability and adjoint-functor theorems when $V = Set$} \subsection{Functor categories, small Projective Limits and Morita Equivalence}
diff 2010-11-01 01:12:36 - revision [ Version = 11 --> Version 12 ] by bci1
diff 2010-11-01 01:10:29 - revision [ Version = 10 --> Version 11 ] by bci1
The isomorphism $[A \times [B, C]] \cong [A,[B,C]]$
diff 2010-11-01 01:08:55 - revision [ Version = 9 --> Version 10 ] by bci1
% almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amsthm} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions % % making logically defined graphics \usepackage{xypic} % there are many more packages, add them here as you need them % define commands here \newcommand{\sR}[0]{\mathbb{R}} \newcommand{\sC}[0]{\mathbb{C}} \newcommand{\sN}[0]{\mathbb{N}} \newcommand{\sZ}[0]{\mathbb{Z}} \newcommand{\R}[0]{\mathbb{R}} \newcommand{\C}[0]{\mathbb{C}} \newcommand{\N}[0]{\mathbb{N}} \newcommand{\Z}[0]{\mathbb{Z}} %\usepackage{bbm} %\newcommand{\N}{\mathbbmss{N}} %\newcommand{\Z}{\mathbbmss{Z}} %\newcommand{\C}{\mathbbmss{C}} %\newcommand{\R}{\mathbbmss{R}} %\newcommand{\Q}{\mathbbmss{Q}} \newcommand*{\norm}[1]{\lVert #1 \rVert} \newcommand*{\abs}[1]{| #1 |} \newcommand{\Map}[3]{#1:#2\to#3} \newcommand{\Emb}[3]{#1:#2\hookrightarrow#3} \newcommand{\Mor}[3]{#2\overset{#1}\to#3} \newcommand{\Cat}[1]{\mathcal{#1}} \newcommand{\Kat}[1]{\mathbf{#1}} \newcommand{\Func}[3]{\Map{#1}{\Cat{#2}}{\Cat{#3}}} \newcommand{\Funk}[3]{\Map{#1}{\Kat{#2}}{\Kat{#3}}} \newcommand{\intrv}[2]{\langle #1,#2 \rangle} \newcommand{\vp}{\varphi} \newcommand{\ve}{\varepsilon} \newcommand{\Invimg}[2]{\inv{#1}(#2)} \newcommand{\Img}[2]{#1[#2]} \newcommand{\ol}[1]{\overline{#1}} \newcommand{\ul}[1]{\underline{#1}} \newcommand{\inv}[1]{#1^{-1}} \newcommand{\limti}[1]{\lim\limits_{#1\to\infty}} \newcommand{\Ra}{\Rightarrow} %fonts \newcommand{\mc}{\mathcal} %shortcuts \newcommand{\Ob}{\mathrm{Ob}} \newcommand{\Hom}{\mathrm{hom}} \newcommand{\homs}[2]{\mathrm{hom(}{#1},{#2}\mathrm )} \newcommand{\Eq}{\mathrm{Eq}} \newcommand{\Coeq}{\mathrm{Coeq}} %theorems \newtheorem{THM}{Theorem} \newtheorem{DEF}{Definition} \newtheorem{PROP}{Proposition} \newtheorem{LM}{Lemma} \newtheorem{COR}{Corollary} \newtheorem{EXA}{Example} %categories \newcommand{\Top}{\Kat{Top}} \newcommand{\Haus}{\Kat{Haus}} \newcommand{\Set}{\Kat{Set}} %diagrams \newcommand{\UnimorCD}[6]{ \xymatrix{ {#1} \ar[r]^{#2} \ar[rd]_{#4}& {#3} \ar@{-->}[d]^{#5} \\ & {#6} } } \newcommand{\RovnostrCD}[6]{ \xymatrix@C=10pt@R=17pt{ & {#1} \ar[ld]_{#2} \ar[rd]^{#3} \\ {#4} \ar[rr]_{#5} && {#6} } } \newcommand{\RovnostrCDii}[6]{ \xymatrix@C=10pt@R=17pt{ {#1} \ar[rr]^{#2} \ar[rd]_{#4}&& {#3} \ar[ld]^{#5} \\ & {#6} } } \newcommand{\RovnostrCDiiop}[6]{ \xymatrix@C=10pt@R=17pt{ {#1} && {#3} \ar[ll]_{#2} \\ & {#6} \ar[lu]^{#4} \ar[ru]_{#5} } } \newcommand{\StvorecCD}[8]{ \xymatrix{ {#1} \ar[r]^{#2} \ar[d]_{#4} & {#3} \ar[d]^{#5} \\ {#6} \ar[r]_{#7} & {#8} } } \newcommand{\TriangCD}[6]{ \xymatrix{ {#1} \ar[r]^{#2} \ar[rd]_{#4}& {#3} \ar[d]^{#5} \\ & {#6} } } \cong
diff 2010-11-01 01:05:24 - revision [ Version = 8 --> Version 9 ] by bci1
diff 2010-11-01 00:55:30 - revision [ Version = 7 --> Version 8 ] by bci1
diff 2010-11-01 00:49:18 - revision [ Version = 6 --> Version 7 ] by bci1
diff 2010-11-01 00:46:03 - revision [ Version = 5 --> Version 6 ] by bci1
diff 2010-11-01 00:44:39 - revision [ Version = 4 --> Version 5 ] by bci1
diff 2010-11-01 00:43:44 - revision [ Version = 3 --> Version 4 ] by bci1
diff 2010-11-01 00:37:59 - revision [ Version = 2 --> Version 3 ] by bci1
diff 2010-11-01 00:36:02 - revision [ Version = 1 --> Version 2 ] by bci1
% this is the default PlanetPhysics preamble. as your % almost certainly you want these \usepackage{amsmath, amssymb, amsfonts, amsthm, amscd, latexsym, enumerate} \usepackage{xypic, xspace} \usepackage[mathscr]{eucal} \usepackage[dvips]{graphicx} \usepackage[curve]{xy} % define commands here \theoremstyle{plain} \newtheorem{lemma}{Lemma}[section] \newtheorem{proposition}{Proposition}[section] \newtheorem{theorem}{Theorem}[section] \newtheorem{corollary}{Corollary}[section] \theoremstyle{definition} \newtheorem{definition}{Definition}[section] \newtheorem{example}{Example}[section] %\theoremstyle{remark} \newtheorem{remark}{Remark}[section] \newtheorem*{notation}{Notation} \newtheorem*{claim}{Claim} \renewcommand{\thefootnote}{\ensuremath{\fnsymbol{footnote}}} \numberwithin{equation}{section} \newcommand{\Ad}{{\rm Ad}} \newcommand{\Aut}{{\rm Aut}} \newcommand{\Cl}{{\rm Cl}} \newcommand{\Co}{{\rm Co}} \newcommand{\DES}{{\rm DES}} \newcommand{\Diff}{{\rm Diff}} \newcommand{\Dom}{{\rm Dom}} \newcommand{\Hol}{{\rm Hol}} \newcommand{\Mon}{{\rm Mon}} \newcommand{\Hom}{{\rm Hom}} \newcommand{\Ker}{{\rm Ker}} \newcommand{\Ind}{{\rm Ind}} \newcommand{\IM}{{\rm Im}} \newcommand{\Is}{{\rm Is}} \newcommand{\ID}{{\rm id}} \newcommand{\grpL}{{\rm GL}} \newcommand{\Iso}{{\rm Iso}} \newcommand{\rO}{{\rm O}} \newcommand{\Sem}{{\rm Sem}} \newcommand{\SL}{{\rm Sl}} \newcommand{\St}{{\rm St}} \newcommand{\Sym}{{\rm Sym}} \newcommand{\Symb}{{\rm Symb}} \newcommand{\SU}{{\rm SU}} \newcommand{\Tor}{{\rm Tor}} \newcommand{\U}{{\rm U}} \newcommand{\A}{\mathcal A} \newcommand{\Ce}{\mathcal C} \newcommand{\D}{\mathcal D} \newcommand{\E}{\mathcal E} \newcommand{\F}{\mathcal F} %\newcommand{\grp}{\mathcal G} \renewcommand{\H}{\mathcal H} \renewcommand{\cL}{\mathcal L} \newcommand{\Q}{\mathcal Q} \newcommand{\R}{\mathcal R} \newcommand{\cS}{\mathcal S} \newcommand{\cU}{\mathcal U} \newcommand{\W}{\mathcal W} \newcommand{\bA}{\mathbb{A}} \newcommand{\bB}{\mathbb{B}} \newcommand{\bC}{\mathbb{C}} \newcommand{\bD}{\mathbb{D}} \newcommand{\bE}{\mathbb{E}} \newcommand{\bF}{\mathbb{F}} \newcommand{\bG}{\mathbb{G}} \newcommand{\bK}{\mathbb{K}} \newcommand{\bM}{\mathbb{M}} \newcommand{\bN}{\mathbb{N}} \newcommand{\bO}{\mathbb{O}} \newcommand{\bP}{\mathbb{P}} \newcommand{\bR}{\mathbb{R}} \newcommand{\bV}{\mathbb{V}} \newcommand{\bZ}{\mathbb{Z}} \newcommand{\bfE}{\mathbf{E}} \newcommand{\bfX}{\mathbf{X}} \newcommand{\bfY}{\mathbf{Y}} \newcommand{\bfZ}{\mathbf{Z}} \renewcommand{\O}{\Omega} \renewcommand{\o}{\omega} \newcommand{\vp}{\varphi} \newcommand{\vep}{\varepsilon} \newcommand{\diag}{{\rm diag}} \newcommand{\grp}{{\mathsf{G}}} \newcommand{\dgrp}{{\mathsf{D}}} \newcommand{\desp}{{\mathsf{D}^{\rm{es}}}} \newcommand{\grpeod}{{\rm Geod}} %\newcommand{\grpeod}{{\rm geod}} \newcommand{\hgr}{{\mathsf{H}}} \newcommand{\mgr}{{\mathsf{M}}} \newcommand{\ob}{{\rm Ob}} \newcommand{\obg}{{\rm Ob(\mathsf{G)}}} \newcommand{\obgp}{{\rm Ob(\mathsf{G}')}} \newcommand{\obh}{{\rm Ob(\mathsf{H})}} \newcommand{\Osmooth}{{\Omega^{\infty}(X,*)}} \newcommand{\grphomotop}{{\rho_2^{\square}}} \newcommand{\grpcalp}{{\mathsf{G}(\mathcal P)}} \newcommand{\rf}{{R_{\mathcal F}}} \newcommand{\grplob}{{\rm glob}} \newcommand{\loc}{{\rm loc}} \newcommand{\TOP}{{\rm TOP}} \newcommand{\wti}{\widetilde} \newcommand{\what}{\widehat} \renewcommand{\a}{\alpha} \newcommand{\be}{\beta} \newcommand{\grpa}{\grpamma} %\newcommand{\grpa}{\grpamma} \newcommand{\de}{\delta} \newcommand{\del}{\partial} \newcommand{\ka}{\kappa} \newcommand{\si}{\sigma} \newcommand{\ta}{\tau} \newcommand{\lra}{{\longrightarrow}} \newcommand{\ra}{{\rightarrow}} \newcommand{\rat}{{\rightarrowtail}} \newcommand{\ovset}[1]{\overset {#1}{\ra}} \newcommand{\ovsetl}[1]{\overset {#1}{\lra}} \newcommand{\hr}{{\hookrightarrow}} \newcommand{\<}{{\langle}} %\newcommand{\>}{{\rangle}} %\usepackage{geometry, amsmath,amssymb,latexsym,enumerate} %\usepackage{xypic} \def\baselinestretch{1.1} \hyphenation{prod-ucts} %\grpeometry{textwidth= 16 cm, textheight=21 cm} \newcommand{\sqdiagram}[9]{$$ \diagram #1 \rto^{#2} \dto_{#4}& #3 \dto^{#5} \\ #6 \rto_{#7} & #8 \enddiagram \eqno{\mbox{#9}}$$ } \def\C{C^{\ast}} \newcommand{\labto}[1]{\stackrel{#1}{\longrightarrow}} %\newenvironment{proof}{\noindent {\bf Proof} }{ \hfill $\Box$ %{\mbox{}} \newcommand{\quadr}[4] {\begin{pmatrix} & #1& \\[-1.1ex] #2 & & #3\\[-1.1ex]& #4& \end{pmatrix}} \def\D{\mathsf{D}}

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