\( \DeclareMathOperator{\Hom}{Hom} \DeclareMathOperator{\uHom}{\,\underline{\!Hom\!}\,} \DeclareMathOperator{\Mor}{Mor} \DeclareMathOperator{\Map}{Map} \DeclareMathOperator{\map}{map} \DeclareMathOperator*{\colim}{colim} \DeclareMathOperator{\id}{id} \DeclareMathOperator{\Id}{Id} \DeclareMathOperator{\Ob}{Ob} \DeclareMathOperator{\comp}{comp} \DeclareMathOperator{\Fun}{Fun} \DeclareMathOperator{\true}{true} \DeclareMathOperator{\Sub}{Sub} \DeclareMathOperator{\Lan}{Lan} \DeclareMathOperator{\Ran}{Ran} \DeclareMathOperator{\PSh}{PSh} \DeclareMathOperator{\Sh}{Sh} \DeclareMathOperator{\Sp}{Sp} \DeclareMathOperator{\Glue}{Glue} \DeclareMathOperator{\Res}{Res} \DeclareMathOperator{\End}{End} \DeclareMathOperator{\oneim}{1im} \DeclareMathOperator{\twoim}{2im} \DeclareMathOperator{\charr}{char} \DeclareMathOperator{\Spec}{Spec} \newcommand{\ProFinSet}{\mathrm{ProFinSet}} \newcommand{\sSet}{\mathrm{sSet}} \newcommand{\Top}{\mathrm{Top}} \newcommand{\deltacat}{\boldsymbol{\Delta}} \newcommand{\Cat}{\mathrm{Cat}} \newcommand{\Set}{\mathrm{Set}} \newcommand{\Ring}{\mathrm{Ring}} \newcommand{\CatMon}{\mathrm{CatMon}} \newcommand{\Cof}{\mathrm{Cof}} \newcommand{\Fib}{\mathrm{Fib}} \newcommand{\Frm}{\mathrm{Frm}} \newcommand{\Loc}{\mathrm{Loc}}\)

Math

I love math, in particular category theory and logic but also geometry. In general I like conceptual clear thinking. For example the last question I tried to answer was: “Can we find a general framework that unifies the process of going from open subsets of \( \mathbb R ^{n} \) to continuous or smooth manifolds and the processes of going from affine schemes to schemes?” See Spaces from Local Models for more.

  1. Category Theory My main source is the nlab. It contains much more content, check it out!
  2. \( 2 \)-Category Theory Again my main source is the nlab.
  3. \( \infty \)-Category Theory My source is Markus Land’s book “Introduction to Infinity-Categories”. Mainly I just rearrange or reformulate the content slightly. Sometimes I change notation or add a result.
  4. Topos Theory My source is the book “Sheaves in Geometry and Logic - A First Introduction to Topos Theory” by Saunders Mac Lane and Ieke Moerdijk.
  5. Type Theory
  6. Miscellaneous

Author: Frederik Gebert

Created: 2025-02-10 Mon 21:45