\phantomsection % black magic to get TOC to point to correct page \markboth{}{\textsc{Index of symbols}} \addcontentsline{toc}{part}{Index of symbols} \chapter*{Index of symbols} % Shorthand for \pageref, we have lots of these. \newcommand{\pg}[1]{p.~\pageref{#1}} % In the next macro whitespace matters, so be careful \newcommand{\symbolindex}[2]{\hbox{\makebox[0.2\textwidth][s]{#1\hfill}\hspace*{2.5em}\parbox[t]{0.65\textwidth}{#2\hfill}}\\[1.5pt]} % The entries in this table are sorted "alphabetically" whatever that means. {\OPTindexfont % Set same font size as for the index % MAKE SURE THERE ARE NO EMPTY LINES, OR ELSE WE GET A PARAGRAPH BREAK. % ALSO, DO NOT INSERT ANY WHITESPACE AT THE BEGINNING OF ARGUMENTS OF \symbolindex \noindent %%%%%%%%%% Equalities %%%%%%%%%% \symbolindex{$x \defeq a$ }{definition, \pg{defn:defeq}} \symbolindex{$a \jdeq b$ }{judgmental equality, \pg{defn:judgmental-equality}} \symbolindex{$a =_A b$ }{identity type, \pg{sec:identity-types}} \symbolindex{$a = b$ }{identity type, \pg{sec:identity-types}} \symbolindex{$x \defid b$ }{propositional equality by definition, \pg{rmk:defid}} \symbolindex{$\idtypevar{A}(a,b)$ }{identity type, \pg{sec:identity-types}} \symbolindex{$\dpath{P}{p}{a}{b}$ }{dependent path type, \pg{eq:dpath}} \symbolindex{$a \neq b$ }{disequality, \pg{sec:disequality}} %%%%%%%%%% Stuff that's hard to alphabetize %%%%%%%%%% \symbolindex{$\refl{x}$ }{reflexivity path at $x$, \pg{sec:identity-types}} \symbolindex{$\opp{p}$ }{path reversal, \pg{lem:opp}} \symbolindex{$p\ct q$ }{path concatenation, \pg{lem:concat}} \symbolindex{$p\leftwhisker r$ }{left whiskering, \pg{thm:EckmannHilton}} \symbolindex{$r\rightwhisker q$ }{right whiskering, \pg{thm:EckmannHilton}} \symbolindex{$r\hct s$ }{horizontal concatenation of 2-paths, \pg{thm:EckmannHilton}} \symbolindex{$g\circ f$ }{composite of functions, \pg{ex:composition}} \symbolindex{$g\circ f$ }{composite of morphisms in a precategory, \pg{ct:precategory}} \symbolindex{$\inv{f}$ }{quasi-inverse of an equivalence, \pg{thm:equiv-eqrel}} \symbolindex{$\inv{f}$ }{inverse of an isomorphism in a precategory, \pg{ct:inv}} %%%%%%%%%% Numbers etc. %%%%%%%%%% \symbolindex{$\emptyt$ }{empty type, \pg{sec:coproduct-types}} \symbolindex{$\unit$ }{unit type, \pg{sec:finite-product-types}} \symbolindex{$\ttt$ }{canonical inhabitant of $\unit$, \pg{sec:finite-product-types}} \symbolindex{$\bool$ }{type of booleans, \pg{sec:type-booleans}} \symbolindex{$\btrue$, $\bfalse$ }{constructors of $\bool$, \pg{sec:type-booleans}} \symbolindex{$\izero$, $\ione$ }{point constructors of the interval $\interval$, \pg{sec:interval}} %%%%%%%%%% A %%%%%%%%%% \symbolindex{$\choice{}$ }{axiom of choice, \pg{eq:ac}} \symbolindex{$\choice{\infty}$ }{``type-theoretic axiom of choice'', \pg{thm:ttac}} \symbolindex{$\acc(a)$ }{accessibility predicate, \pg{defn:accessibility}} \symbolindex{$P \land Q$ }{logical conjunction (``and''), \pg{defn:logical-notation}} \symbolindex{$\apfunc{f}(p)$ or $\ap{f}{p}$ }{application of $f:A\to B$ to $p:\id[A]xy$, \pg{lem:map}} \symbolindex{$\apd{f}{p}$ }{application of $f:\prd{a:A} B(a)$ to $p:\id[A]xy$, \pg{lem:mapdep}} % This is not currently a distinctive notation that someone would look up % $\aptwo{f}{p}$ & two-dimensional $\apfunc{}$, \pg{thm:ap2} % \\ \symbolindex{$\apdtwo{f}{p}$ }{two-dimensional dependent $\apfunc{}$, \pg{thm:apd2}} \symbolindex{$x\apart y$ }{apartness of real numbers, \pg{apart}} %%%%%%%%%% B %%%%%%%%%% \symbolindex{$\base$ }{basepoint of $\Sn^1$, \pg{sec:intro-hits}} \symbolindex{$\base$ }{basepoint of $\Sn^2$, \pg{s2a} and \pg{s2b}} \symbolindex{$\biinv(f)$ }{proposition that $f$ is bi-invertible, \pg{defn:biinv}} \symbolindex{$x \bisim y$ }{bisimulation, \pg{def:bisimulation}} \symbolindex{$\blank$ }{blank used for implicit $\lambda$-abstractions, \pg{blank}} %%%%%%%%%% C %%%%%%%%%% \symbolindex{$\CAP$ }{type of Cauchy approximations, \pg{cauchy-approximations}} \symbolindex{$\card$ }{type of cardinal numbers, \pg{defn:card}} \symbolindex{$\modal A$ }{reflector or modality applied to $A$, \pg{defn:reflective-subuniverse} and \pg{defn:modality}} \symbolindex{$\cocone{X}{Y}$ }{type of cocones, \pg{defn:cocone}} % Not used %\symbolindex{ % \cone{X}{Y}$ %}{ % type of cones %} \symbolindex{$\code$ }{family of codes for paths, \pg{sec:compute-coprod}, \pg{S1-universal-cover}, \pg{sec:general-encode-decode}} \symbolindex{$A \setminus B$ }{subset complement, \pg{complement}} \symbolindex{$\cons(x,\ell)$ }{concatenation constructor for lists, \pg{lst} and \pg{lst-freemonoid}} \symbolindex{$\contr_x$ }{path to the center of contraction, \pg{defn:contractible}} \symbolindex{$\mathcal{F}\cover\pairr{J, \mathcal{G}}$ }{inductive cover, \pg{defn:inductive-cover}} \symbolindex{$\dcut(L,U)$ }{the property of being a Dedekind cut, \pg{defn:dedekind-reals}} \symbolindex{$\surr{L}{R}$ }{cut defining a surreal number, \pg{surreal-cut}} %%%%%%%%%% D %%%%%%%%%% \symbolindex{$\dgr{X}$ }{morphism reversal in a $\dagger$-category, \pg{sec:dagger-categories}} \symbolindex{$\decode$ }{decoding function for paths, \pg{sec:compute-coprod}, \pg{S1-universal-cover}, \pg{sec:general-encode-decode}} %%%%%%%%%% E %%%%%%%%%% \symbolindex{$\encode$ }{encoding function for paths, \pg{sec:compute-coprod}, \pg{S1-universal-cover}, \pg{sec:general-encode-decode}} \symbolindex{$\mreturn^\modal_A$ or $\mreturn_A$ }{the function $A\to\modal A$, \pg{defn:reflective-subuniverse} and \pg{defn:modality}} \symbolindex{$A \epi B$ }{epimorphism or surjection} \symbolindex{$\noeq(x,y)$ }{path constructor of the surreals, \pg{defn:surreals}} \symbolindex{$\rceq(u,v)$ }{path constructor of the Cauchy reals, \pg{defn:cauchy-reals}} \symbolindex{$a \eqr b$ }{an equivalence relation, \pg{equivalencerelation}} \symbolindex{$\eqv{X}{Y}$ }{type of equivalences, \pg{eq:eqv}} \symbolindex{$\texteqv{X}{Y}$ }{type of equivalences (same as $\eqv{X}{Y}$)} \symbolindex{$\cteqv{A}{B}$ }{type of equivalences of categories, \pg{ct:equiv}} \symbolindex{$P \Leftrightarrow Q$ }{logical equivalence, \pg{defn:logical-notation}} \symbolindex{$\exis{x:A} B(x)$ }{logical notation for mere existential, \pg{defn:logical-notation}} \symbolindex{$\extend f$ }{extension of $f:A\to B$ along $\eta_A$, \pg{extend}} %%%%%%%%%% F %%%%%%%%%% \symbolindex{$\bot$ }{logical falsity, \pg{defn:logical-notation}} \symbolindex{$\hfib{f}{b}$ }{fiber of $f:A\to B$ at $b:B$, \pg{defn:homotopy-fiber}} \symbolindex{$\Fin(n)$ }{standard finite type, \pg{fin}} \symbolindex{$\fall{x:A} B(x)$ }{logical notation for dependent function type, \pg{defn:logical-notation}} \symbolindex{$\funext$ }{function extensionality, \pg{axiom:funext}} \symbolindex{$A\to B$ }{function type, \pg{sec:function-types}} \symbolindex{$B^A$ }{functor precategory, \pg{ct:functor-precat}} %%%%%%%%%% G %%%%%%%%%% \symbolindex{$\glue$ }{path constructor of $A \sqcup^C B$, \pg{sec:colimits}} %%%%%%%%%% H %%%%%%%%%% \symbolindex{$\happly$ }{function making a path of functions into a homotopy, \pg{eq:happly}} \symbolindex{$\hom_A(a,b)$ }{hom-set in a precategory, \pg{ct:precategory}} \symbolindex{$f \htpy g$ }{homotopy between functions, \pg{defn:homotopy}} %%%%%%%%%% I %%%%%%%%%% \symbolindex{$\interval$ }{the interval type, \pg{sec:interval}} \symbolindex{$\idfunc[A]$ }{the identity function of $A$, \pg{idfunc}} \symbolindex{$1_a$ }{identity morphism in a precategory, \pg{ct:precategory}} \symbolindex{$\idtoeqv$ }{function $(A=B)\to(\eqv A B)$ which univalence inverts, \pg{eq:uidtoeqv}} \symbolindex{$\idtoiso$ }{function $(a=b) \to (a\cong b)$ in a precategory, \pg{ct:idtoiso}} \symbolindex{$\im(f)$ }{image of map $f$, \pg{defn:modal-image}} \symbolindex{$\im_n(f)$ }{$n$-image of map $f$, \pg{defn:modal-image}} \symbolindex{$P \Rightarrow Q$ }{logical implication (``implies''), \pg{defn:logical-notation}} \symbolindex{$a \in P$ }{membership in a subset or subtype, \pg{membership}} \symbolindex{$x\in v$ }{membership in the cumulative hierarchy, \pg{V-membership}} \symbolindex{$x\bin v$ }{resized membership, \pg{resized-membership}} \symbolindex{$\ind{\emptyt}$ }{induction for ${\emptyt}$, \pg{defn:induction-emptyt},} \symbolindex{$\ind{\unit}$ }{induction for ${\unit}$, \pg{defn:induction-unit},} \symbolindex{$\ind{\bool}$ }{induction for ${\bool}$, \pg{defn:induction-bool},} \symbolindex{$\ind{\nat}$ }{induction for ${\nat}$, \pg{defn:induction-nat}, and} \symbolindex{$\indid{A}$ }{path induction for $=_A$, \pg{defn:induction-ML-id},} \symbolindex{$\indidb{A}$ }{based path induction for $=_A$, \pg{defn:induction-PM-id},} \symbolindex{$\ind{A \times B}$ }{induction for ${A \times B}$, \pg{defn:induction-times},} \symbolindex{$\ind{\sm{x:A} B(x)}$ }{induction for ${\sm{x:A} B}$, \pg{defn:induction-sm},} \symbolindex{$\ind{A + B}$ }{induction for ${A + B}$, \pg{defn:induction-plus},} \symbolindex{$\ind{\wtype{x:A} B(x)}$ }{induction for ${\wtype{x:A} B}$, \pg{defn:induction-wtype}} \symbolindex{$\ordsl{A}{a}$ }{initial segment of an ordinal, \pg{initial-segment}} \symbolindex{$\inj(A,B)$ }{type of injections, \pg{inj}} \symbolindex{$\inl$ }{first injection into a coproduct, \pg{sec:coproduct-types}} \symbolindex{$\inr$ }{second injection into a coproduct, \pg{sec:coproduct-types}} \symbolindex{$A \cap B$ }{intersection of subsets, \pg{intersection}, classes, \pg{class-intersection}, or intervals, \pg{interval-intersection}} \symbolindex{$\iscontr(A)$ }{proposition that $A$ is contractible, \pg{defn:contractible}} \symbolindex{$\isequiv(f)$ }{proposition that $f$ is an equivalence, \pg{basics-isequiv}, \pg{cha:equivalences}, and \pg{sec:concluding-remarks}} \symbolindex{$\ishae(f)$ }{proposition that $f$ is a half-adjoint equivalence, \pg{defn:ishae}} \symbolindex{$a\cong b$ }{type of isomorphisms in a (pre)category, \pg{ct:isomorphism}} \symbolindex{$A\cong B$ }{type of isomorphisms between precategories, \pg{ct:isocat}} \symbolindex{$A\cong B$ }{type of isomorphisms between sets, \pg{basics:iso}} \symbolindex{$a\unitaryiso b$ }{type of unitary isomorphisms, \pg{ct:unitary}} \symbolindex{$\isotoid$ }{inverse of $\idtoiso$ in a category, \pg{isotoid}} \symbolindex{$\istype{n}(X)$ }{proposition that $X$ is an $n$-type, \pg{def:hlevel}} \symbolindex{$\isprop(A)$ }{proposition that $A$ is a mere proposition, \pg{defn:isprop}} \symbolindex{$\isset(A)$ }{proposition that $A$ is a set, \pg{defn:set}} %%%%%%%%%% J %%%%%%%%%% \symbolindex{$A*B$ }{join of $A$ and $B$, \pg{join}} %%%%%%%%%% K %%%%%%%%%% \symbolindex{$\ker(f)$ }{kernel of a map of pointed sets, \pg{kernel}} %%%%%%%%%% L %%%%%%%%%% \symbolindex{$\lam{x} b(x)$ }{$\lambda$-abstraction, \pg{eq:lambda-abstraction}} \symbolindex{$\lcoh{f}{g}{\eta}$ }{type of left adjoint coherence data, \pg{defn:lcoh-rcoh}} \symbolindex{$\LEM{}$ }{law of excluded middle, \pg{eq:lem}} \symbolindex{$\LEM{\infty}$ }{inconsistent propositions-as-types \LEM{}, \pg{thm:not-lem} and \pg{lem-infty}} \symbolindex{$x < y$ }{strict inequality on natural numbers, \pg{leq-nat}, ordinals, \pg{sec:ordinals}, Cauchy reals, \pg{lt-RC}, surreals, \pg{defn:surreals}, etc.} \symbolindex{$x \le y$ }{non-strict inequality on natural numbers, \pg{leq-nat}, Cauchy reals, \pg{leq-RC}, surreals, \pg{defn:surreals}, etc.} \symbolindex{$\preceq$, $\prec$ }{recursive versions of $\le$ and $<$ for surreals, \pg{defn:No-codes}} \symbolindex{$\ble$, $\blt$, $\bble$, $\bblt$ }{orderings on codomain of $\NO$-recursion, \pg{NO-recursion}} \symbolindex{$\rclim(x)$ }{limit of a Cauchy approximation, \pg{defn:cauchy-reals}} \symbolindex{$\linv(f)$ }{type of left inverses to $f$, \pg{defn:linv-rinv}} \symbolindex{$\lst{X}$ }{type of lists of elements of $X$, \pg{lst} and \pg{lst-freemonoid}} \symbolindex{$\lloop$ }{path constructor of $\Sn^1$, \pg{sec:intro-hits}} %%%%%%%%%% M %%%%%%%%%% \symbolindex{$\Map_*(A,B)$ }{type of based maps, \pg{based-maps}} \symbolindex{$x\mapsto b$ }{alternative notation for $\lambda$-abstraction, \pg{mapsto}} \symbolindex{$\max(x,y)$ }{maximum in some ordering, e.g.\ \pg{ordered-field} and \pg{leq-RC}} \symbolindex{$\merid(a)$ }{meridian of $\susp A$ at $a:A$, \pg{sec:suspension}} \symbolindex{$\min(x,y)$ }{minimum in some ordering, e.g.\ \pg{ordered-field} and \pg{leq-RC}} \symbolindex{$A \mono B$ }{monomorphism or embedding} %%%%%%%%%% N %%%%%%%%%% \symbolindex{$\N$ }{type of natural numbers, \pg{sec:inductive-types}} \symbolindex{$\north$ }{north pole of $\susp A$, \pg{sec:suspension}} \symbolindex{$\natw$, $\zerow$, $\sucw$ }{natural numbers encoded as a $W$-type, \pg{natw}} \symbolindex{$\nalg$ }{type of $\nat$-algebras, \pg{defn:nalg}} \symbolindex{$\nhom(C,D)$ }{type of $\nat$-homomorphisms, \pg{defn:nhom}} \symbolindex{$\nil$ }{empty list, \pg{lst} and \pg{lst-freemonoid}} \symbolindex{$\NO$ }{type of surreal numbers, \pg{defn:surreals}} \symbolindex{$\neg P$ }{logical negation (``not''), \pg{defn:logical-notation}} \symbolindex{$\typele{n}$, $\typeleU{n}$ }{universe of $n$-types, \pg{universe-of-ntypes}} %%%%%%%%%% O %%%%%%%%%% \symbolindex{$\Omega(A,a)$, $\Omega A$ }{loop space of a pointed type, \pg{def:loopspace}} \symbolindex{$\Omega^k(A,a)$, $\Omega^k A$ }{iterated loop space, \pg{def:loopspace}} \symbolindex{$A\op$ }{opposite precategory, \pg{ct:opposite-category}} \symbolindex{$P \lor Q$ }{logical disjunction (``or''), \pg{defn:logical-notation}} \symbolindex{$\ord$ }{type of ordinal numbers, \pg{ord}} %%%%%%%%%% P %%%%%%%%%% \symbolindex{$\pairr{a,b}$ }{(dependent) pair, \pg{sec:finite-product-types} and \pg{defn:dependent-pair}} \symbolindex{$\pairpath$ }{constructor for $=_{A \times B}$, \pg{defn:pairpath}} \symbolindex{$\pi_n(A)$ }{$n^{\mathrm{th}}$ homotopy group of $A$, \pg{thm:homotopy-groups} and \pg{def-of-homotopy-groups}} \symbolindex{$\power A$ }{power set, \pg{powerset}} \symbolindex{$\powerp A$ }{merely-inhabited power set, \pg{inhabited-powerset}} \symbolindex{$\Zpred$ }{predecessor function $\Z\to\Z$, \pg{subsec:pi1s1-encode-decode}} \symbolindex{$A\times B$ }{cartesian product type, \pg{sec:finite-product-types}} \symbolindex{$\prd{x:A} B(x)$ }{dependent function type, \pg{sec:pi-types}} \symbolindex{$\proj1(t)$ }{the first projection from a pair, \pg{defn:proj} and \pg{defn:dependent-proj1}} \symbolindex{$\proj2(t)$ }{the second projection from a pair, \pg{defn:proj} and \pg{defn:dependent-proj1}} \symbolindex{$\prop$, $\propU$ }{universe of mere propositions, \pg{propU}} \symbolindex{$A \times_C B$ }{pullback of $A$ and $B$ over $C$, \pg{eq:defn-pullback}} \symbolindex{$A \sqcup^C B$ }{pushout of $A$ and $B$ under $C$, \pg{sec:colimits}} %%%%%%%%%% Q %%%%%%%%%% \symbolindex{$\Q$ }{type of rational numbers, \pg{sec:field-rati-numb}} \symbolindex{$\Qp$ }{type of positive rational numbers, \pg{positive-rationals}} \symbolindex{$\qinv(f)$ }{type of quasi-inverses to $f$, \pg{qinv}} \symbolindex{$A/R$ }{quotient of a set by an equivalence relation, \pg{sec:set-quotients}} \symbolindex{$A\sslash R$ }{alternative definition of quotient, \pg{def:VVquotient}} %%%%%%%%%% R %%%%%%%%%% \symbolindex{$\R$ }{type of real numbers (either), \pg{sec:compactness-interval}} \symbolindex{$\RC$ }{type of Cauchy real numbers, \pg{defn:cauchy-reals}} \symbolindex{$\RD$ }{type of Dedekind real numbers, \pg{defn:dedekind-reals}} \symbolindex{$\rcrat(q)$ }{rational number regarded as a Cauchy real, \pg{defn:cauchy-reals}} \symbolindex{$\rcoh{f}{g}{\epsilon}$ }{type of right adjoint coherence data, \pg{defn:lcoh-rcoh}} \symbolindex{$\rec{\emptyt}$ }{recursor for ${\emptyt}$, \pg{defn:recursor-emptyt}} \symbolindex{$\rec{\unit}$ }{recursor for ${\unit}$, \pg{defn:recursor-unit}} \symbolindex{$\rec{\bool}$ }{recursor for ${\bool}$, \pg{defn:recursor-bool}} \symbolindex{$\rec{\nat}$ }{recursor for ${\nat}$, \pg{defn:recursor-nat}} \symbolindex{$\rec{A \times B}$ }{recursor for ${A \times B}$, \pg{defn:recursor-times}} \symbolindex{$\rec{\sm{x:A} B(x)}$ }{recursor for ${\sm{x:A} B}$, \pg{defn:recursor-sm}} \symbolindex{$\rec{A + B}$ }{recursor for ${A + B}$, \pg{defn:recursor-plus}} \symbolindex{$\rec{\wtype{x:A} B(x)}$ }{recursor for ${\wtype{x:A} B}$, \pg{defn:recursor-wtype}} \symbolindex{$\rinv$ }{type of right inverses to $f$, \pg{defn:linv-rinv}} %%%%%%%%%% S %%%%%%%%%% \symbolindex{$\south$ }{south pole of $\susp A$, \pg{sec:suspension}} \symbolindex{$\Sn^n$ }{$n$-dimensional sphere, \pg{sec:circle}} \symbolindex{$\seg$ }{path constructor of the interval $\interval$, \pg{sec:interval}} \symbolindex{$\set$, $\setU$ }{universe of sets, \pg{setU}} \symbolindex{$\uset$ }{category of sets, \pg{ct:precatset}} \symbolindex{$\vset(A,f)$ }{constructor of the cumulative hierarchy, \pg{defn:V}} \symbolindex{$x\sim_\epsilon y$ }{relation of $\epsilon$-closeness for $\RC$, \pg{defn:cauchy-reals}} \symbolindex{$x\approx_\epsilon y$ }{recursive version of $\sim_\epsilon$, \pg{defn:RC-approx}} \symbolindex{$\bsim_\epsilon$ or $\bbsim_\epsilon$ }{closeness relations on codomain of $\RC$-recursion, \pg{RC-recursion}} \symbolindex{$A\wedge B$ }{smash product of $A$ and $B$, \pg{smash}} \symbolindex{$\setof{x : A | P(x)}$ }{subset type, \pg{defn:setof}} \symbolindex{$\setof{ f(x) | P(x)}$ }{image of a subset, \pg{subset-image}} \symbolindex{$B \subseteq C$ }{containment of subset types, \pg{subset}} \symbolindex{$(q,r)\subseteq (s,t)$ }{inclusion of intervals, \pg{interval-subset}} \symbolindex{$\suc$ }{successor function $\N\to\N$, \pg{sec:inductive-types}} \symbolindex{$\Zsuc$ }{successor function $\Z\to\Z$, \pg{sec:pi1s1-initial-thoughts}} \symbolindex{$A+B$ }{coproduct type, \pg{sec:coproduct-types}} \symbolindex{$\sm{x:A} B(x)$ }{dependent pair type, \pg{sec:sigma-types}} \symbolindex{$\supp(a, f)$ }{constructor for $W$-type, \pg{defn:supp}} \symbolindex{$\surf$ }{2-path constructor of $\Sn^2$, \pg{s2a} and \pg{s2b}} \symbolindex{$\susp A$ }{suspension of $A$, \pg{sec:suspension}} %%%%%%%%%% T %%%%%%%%%% \symbolindex{$\total{f}$ }{induced map on total spaces, \pg{defn:total-map}} \symbolindex{$\trans{p}{u}$ }{transport of $u:P(x)$ along $p:x=y$, \pg{lem:transport}} \symbolindex{$\transfib{P}{p}{u}$ }{transport of $u:P(x)$ along $p:x=y$, \pg{lem:transport}} \symbolindex{$\transtwo{X}{Y}$ }{two-dimensional transport, \pg{thm:transport2}} \symbolindex{$\transconst{X}{Y}{Z}$ }{transporting in a constant family, \pg{thm:trans-trivial}} \symbolindex{$\trunc{n}{A}$ }{$n$-truncation of $A$, \pg{sec:truncations}} \symbolindex{$\tproj[A]{n}{a}$, $\tproj{n}{a}$ }{image of $a:A$ in $\trunc n A$, \pg{sec:truncations}} \symbolindex{$\brck{A}$ }{propositional truncation of $A$, \pg{subsec:prop-trunc} and \pg{sec:hittruncations}} \symbolindex{$\bproj{a}$ }{image of $a:A$ in $\brck A$, \pg{subsec:prop-trunc} and \pg{sec:hittruncations}} \symbolindex{$\top$ }{logical truth, \pg{defn:logical-notation}} %%%%%%%%%% U %%%%%%%%%% \symbolindex{$\nameless$ }{an unnamed object or variable} \symbolindex{$A \cup B$ }{union of subsets, \pg{union}} \symbolindex{$\uniq{A\times B}$ }{uniqueness principle for the product $A\times B$, \pg{uniquenessproduct}} \symbolindex{$\uniq{\unit}$ }{uniqueness principle for $\unit$, \pg{uniquenessunit}} \symbolindex{$\UU$ }{universe type, \pg{sec:universes}} \symbolindex{$\modaltype$ }{universe of modal types, \pg{eq:modaltype}} \symbolindex{$\pointed\type$ }{universe of pointed types, \pg{def:pointedtype}} \symbolindex{$\ua$ }{inverse to $\idtoeqv$ from univalence, \pg{ua}} %%%%%%%%%% V %%%%%%%%%% \symbolindex{$V$ }{cumulative hierarchy, \pg{defn:V}} %%%%%%%%%% W %%%%%%%%%% \symbolindex{$\walg(A,B)$ }{type of $w$-algebras, \pg{walg}} \symbolindex{$\whom_{A,B}(C,D)$ }{type of $\w$-homomorphisms, \pg{whom}} \symbolindex{$\wtype{x:A} B(x)$ }{$W$-type (inductive type), \pg{sec:w-types}} \symbolindex{$A\vee B$ }{wedge of $A$ and $B$, \pg{wedge}} %%%%%%%%%% X %%%%%%%%%% %%%%%%%%%% Y %%%%%%%%%% \symbolindex{$\y$ }{Yoneda embedding, \pg{ct:yoneda}} %%%%%%%%%% Z %%%%%%%%%% \symbolindex{$\Z$ }{type of integers, \pg{defn-Z}}} %%% Local Variables: %%% mode: latex %%% TeX-master: "hott-online" %%% End: