Notes and Preprints
My private study note.
(Updated Feb. 22, 2019)
All chapters are incomplete.
The contents are as follows.

Chapter 1 On the notion of schemes of graded rings
(Source; DemazureGabriel "Introduction to Algebraic Geometry and Algebraic Groups", Chapter 1 )

Chapter 2 Grothendiek Topos (Sources; "SGA4", EXPOSE II,
III, IV and MacLaneMoerdijk "Sheaves in Geometry and Logic")

Chapter 3 Elementary Topos (Source; Johnstone "Topos Theory", Chapter 1 )

Chapter 4 Topologies and sheaves (Source; Johnstone "Topos Theory", Chapter 3 )

Chapter 5 Internal Categories (Source; Johnstone "Topos Theory", Chapter 2 )

Chapter 6 Galois category (Source; "SGA1", EXPOSE V)

Chapter 7 Model categories for the working mathematicians
(Source; Quillen "Homotopical Algebra", M. Hovey "Model Categories")

Chapter 8 Study on fibered categories

Chapter 9 Representations of internal categories
 Appendix Categories for mathematician reading SGA
(Sources; "SGA4", EXPOSE I, MacLane "Categories for the Working
Mathematician" GTM236, Barr "Exact categories" LNM236, Johnstone
"Adjoint lifting theorems for category of algebras", Bull. Lond. Math.
Soc. 7 (1975), 294297, etc.)
Lecture notes and slides

Complex cobordism theory and groupoid of formal groups (Updated March 7, 2007)

Bar spectral sequence (Updated Septmber 1, 2004)

Model categories for the working mathematicians March 1516, 2010
[Keynote file] (Updated March 20, 2015)

Toward a representation theory of the group scheme represented by the dual Steenrod algebra March 19, 2015
[Keynote file] (Updated March 20, 2015)

Representations of the group represented by the dual Steenrod algebra November 12, 2016
[Keynote file] (Updated November 29,2021)

A Convenient Fibered Category for Representation Theory July 12, 2017
[Keynote file] (Updated July 28, 2017)

Cohomology Theory and Representation Theory January 25, 2018
[Keynote file] (Updated May 16, 2019)

Representation Theory of Hopf Algebroids September 20, 2018
[Keynote file] (Updated October 4, 2018)

Representations of Hopf algebras as group actions June 28, 2019
[Keynote file] (Updated July 1, 2019)

The Steenrod Algebra from the Group Theoretical Viewpoint October 27, 2019
[Keynote file] (Updated November 29,2021)

Representation theory of internal categories and its application to comodules over Hopf algebroids November 9, 2019
[Keynote file] (Updated November 29,2021)

On the fibered category of smooth maps and actions of diffeological groupoids Nobember 7, 2020
[Keynote file] (Updated November 29,2021)
My paper on the Web

On excess filtration on the Steenrod algebra Local copy (Updated November 29,2021)
Link to Geometry & Topology site

The Steenrod algebra from the group theoretical viewpoint
Research note(in progress, highly incomplete)

Representations of the Steenrod group
(Updated November 29,2021)

Notes on representation theory of internal categories (Updated November 29,2021)
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